Bibliometrics as a research field: A course on theory and application of bibliometric indicators

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BIBLIOMETRICS AS A RESEARCH FIELD
A course on theory and application of bibliometric indicators
W. GLÄNZEL
COURSE HANDOUTS
2003

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CONTENT
General Introduction ....................................................................................................5
1. Historical remarks..................................................................................................6
1.1 The origin of the name ‘Bibliometrics’ .................................................................. 6
1.2 The pioneers in bibliometrics................................................................................. 6
1.3 Bibliometrics since deSolla Price .......................................................................... 8
1.4 The three “components” of present-day bibliometrics .......................................... 9
2. The elements of bibliometric research and their mathematical background.......11
2.1 Basic concepts of elements, units and measures of bibliometric research .......... 12
2.2 Data sources of bibliometric research................................................................. 13
2.3 Minimum bibliographic description for paper identification .............................. 16
2.4 Mathematical models and the “distributional” approach................................... 17
2.4.1 Historical sketch of mathematical methods used in bibliometrics....................... 17
2.4.2 Basic postulates and the “axiomatic approach” to bibliometrics ....................... 20
2.4.3 Deterministic models of productivity and citation processes............................... 23
2.4.4 The stochastic approach to bibliometrics ........................................................... 28
3. Indicators of publication activity.........................................................................36
3.1 Counting schemes and main levels of aggregation.............................................. 36
3.2 Problems of subject assignment........................................................................... 38
3.3 Statistics on scientific productivity: Frequency distributions
vs. rank statistics ................................................................................................. 40
3.4 Factors influencing publication activity, subject characteristics
in publication activity........................................................................................... 45
3.5 Publication profiles of institutional and national research activity..................... 48
3.5.1 Publication profiles by discipline......................................................................... 49
3.5.2 Publication profiles by sectors............................................................................. 51
3.5.3 Publication profiles by funding............................................................................ 51
3.5.4 Characterising research dynamics of institutions, regions or countries ............. 52
4. Indicators of citation impact................................................................................53
4.1. The notion of citations in information science and bibliometrics........................ 53
4.2 The role of self-citations....................................................................................... 56
4.3 Factors influencing citation impact ..................................................................... 60
4.4 Journal citation measures: the Impact Factor..................................................... 63
4.5 Relative citation indicators .................................................................................. 66
5. Indicators of scientific collaboration ...................................................................73
5.1 Co-authorship as a measure of scientific collaboration ...................................... 73
5.2 Indicators of co-operativity and co-publication networks ................................... 76
6. Indicators and advanced data-analytical methods ...............................................81
6.1 Bibliometric transaction matrices ....................................................................... 81
6.2 Bibliographic coupling and co-citation analysis ................................................. 83
6.3 Co-word, Co-heading and Co-author Clustering Techniques............................. 85
6.4 Techniques of Matrix Analysis............................................................................. 86

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7. The borderland of bibliometric research..............................................................89
7.1. Linkage between science and technology ............................................................ 89
7.2. New horizons: bibliometric methods in webometrics .......................................... 91
8. Introduction to bibliometric technology .............................................................93
8.1 Outlines of cleaning-up and computerised data processing of
bibliographic data................................................................................................ 93
8.2 Bibliometric sortware .......................................................................................... 97
References.................................................................................................................103
APPENDIX: List of recommended readings............................................................111

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GENERAL INTRODUCTION
Bibliometrics has become a standard tool of science policy and research management in the
last decades. All significant compilations of science indicators heavily rely on publication and
citation statistics and other, more sophisticated bibliometric techniques.
Examples for such compilations are:
− National Science Board
− Observatoire des Sciences et des Techniques
− European Report on S&T Indicators
− Het Nederlands Observatorium van Wetenschap en Technologie: Wetenschaps- en
Technologie-Indicatoren
− Vlaams Indicatorenboek
In addition, many extensive bibliometric studies of important science fields appeared during
the last two decades. Aim of these studies was to measure national research performance in
the international context or to describe the development of a science field with the help of
bibliometric means (for instance, Braun et al., 1987).
It is a common misbelief that bibliometrics is nothing else but publication and citation based
gauging of scientific performance or compiling of cleaned-up bibliographies on research
domains extended by citation data. In fact, scientometrics is a multifaceted endeavour
encompassing subareas such as structural, dynamic, evaluative and predictive scientometrics.
Structural scientometrics came up with results like the re-mapping of the epistemological
structure of science based, for instance, on co-citation, ”bibliographic coupling” techniques or
co-word techniques. Dynamic scientometrics constructed sophisticated models of scientific
growth, obsolescence, citation processes, etc. These models are not only of theoretical interest
but can also be usefully applied in evaluation and prediction.
Beyond policy relevant applications of bibliometric results, there are recently important
applications in the context of studying the linkage between science and technology, or
applications to related fields such as library and information science and most recently also
Webometrics. Examples for the latter ones are the large ongoing projects EICSTES
(European Indicators, Cyberspace and the Science-Technology- Economy System) and
WISER (Web indicators for scientific, technology and innovation research).
Today, bibliometrics is one of the rare truly interdisciplinary research fields to extend to
almost all scientific fields. Bibliometric methodology comprises components from
mathematics, social sciences, natural sciences, engineering and even life sciences. The
following pages will provide a systematic description of the research structure of the field and
a detailed overview of the state-of-the-art in bibliometric methodology.

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1. HISTORICAL REMARKS
1.1 The origin of the name ‘Bibliometrics’
The terms bibliometrics and scientometrics were almost simultaneously introduced by
Pritchard and by Nalimov and Mulchenko in 1969. While Pritchard explained the term
bibliometrics as “the application of mathematical and statistical methods to books and other
media of communication”, Nalimov and Mulchenko defined scientometrics as “the application
of those quantitative methods which are dealing with the analysis of science viewed as an
information process”. According to these interpretations the speciality scientometrics is
restricted to the measurement of science communication, whereas bibliometrics is designed to
deal with more general information processes. The anyhow fuzzy borderlines between the two
specialities almost vanished during the last three decades, and nowadays both terms are used
almost as synonyms. Instead, the field informetrics took the place of the originally broader
speciality bibliometrics. The term informetrics was adopted by VINITI (Gorkova, 1988) and
stands for a more general subfield of information science dealing with mathematical-
statistical analysis of communication processes in science. In contrast to the original
definition of bibliometrics, informetrics also deals with electronic media and thus includes
topics such as the statistical analysis of the (scientific) text and hypertext systems, library
circulations, information measures in electronic libraries, models for Information Production
Processes and quantitative aspects of information retrieval as well.
1.2 The pioneers of bibliometrics
The statistical analysis of scientific literature began almost 50 years before the term
“bibliometrics” was coined. In 1926, Alfred J. Lotka published his pioneering study on the
frequency distribution of scientific productivity determined from a decennial index (1907-
1916) of Chemical Abstracts. Lotka concluded that
“the number (of authors) making n contributions is about 1/n² of those making one;
and the proportion of all contributors, that makes a single contribution, is about 60 per
cent.”
This result can be considered as a rule of thumb even today, 75 years after its publication.
At almost the same time, in 1927, Gross and Gross published their citation-based study in
order to aid the decision which chemistry periodicals should best purchased by small college
libraries. In particular, they examined 3633 citations from the 1926 volume of the Journal of
the American Chemical Society. This study is considered the first citation analysis, although it
is not a citation analysis in the sense of present-day bibliometrics.
Eight years after Lotka’s article appeared, Bradford (1934) published his study on the
frequency distribution of papers over journals. He found that
“if scientific journals are arranged in order of decreasing productivity on a given
subject, they may be divided into a nucleus of journals more particularly devoted to the
subject and several groups or zones containing the same number of articles as the
nucleus when the numbers of periodicals in the nucleus and the succeeding zones will
be as 1: b : b² …”

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Zipf (1949) formulated an interesting law in bibliometrics and quantitative linguistics that he
derived from the study of word frequency in a text. According to Zipf rf = C, where r is the
rank of a word, f is the frequency of occurrence of the word and C is a constant that depends
on the text being analysed. It can be considered a generalisation of the laws by Lotka and
Bradford. He formulated the following underlying principle of his law although he has never
shown how this principle applies to his equation.
"The Principle of Least Effort means… that a person…will strive to solve his problems
in such a way as to minimize the total work that he must expend in solving both his
immediate problems and his probable future problems…." (Zipf, 1949).
Figure 1 First page of Alfred Lotka’s famous article on scientific productivity of chemists
Relatively little attention has been paid to these results. The causes for this phenomenon are
threefold.
1. These papers appeared when traditional methods of information retrieval were still
sufficient,
2. they applied to different phenomena and the interrelation between these laws which
was not completely recognised;

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3. and financing systems for scientific research did not yet stand need of quantitative or
even sophisticated statistical methods.
This situation dramatically changed when Derek deSolla Price published his fundamental
work in bibliometrics.
1.3 Bibliometrics since deSolla Price
In his book entitled “Little Science – Big Science” (1963), Derek deSolla Price analysed the
recent system of science communication and thus presented the first systematic approach to
the structure of modern science applied to the science as a whole.
At the same time, he laid the foundation of modern research evaluation techniques. DeSolla
Price’ work was more than pioneering; it was revolutionary. Time was now ripe for the
reception of his ideas since globalisation of science communication, the growth of knowledge
and published results, increasing specialisation as well as growing importance of
interdisciplinarity in scientific research reached a stage where scientific information retrieval
began to fail and funding systems based on personal knowledge and evaluations by peer
reviews became more and more difficult.
At that time, most basic models for scientific communication were developed. Among these
are first models for essential concepts in scientific communication like growth and ageing of
information. Literature and information was assumed to grow exponentially, but in individual
research disciplines the growth can also be linear or logistic. Finally, the logistic model has
been widely accepted since both exponential and linear growth can be considered special
phases within the logistic model. The concept of ageing or obsolescence is intimately linked
with the growth of science. In information science and bibliometrics, changing frequency of
citations given or received over time is assumed to reflect ageing of scientific literature. Some
authors have downright considered growth and obsolescence inverse functions, the faster
growth of literature in a field, the faster it ages and the literature becomes obsolete in a shorter
time (Brookes, 1970, Egghe, 1993, Kärki and Kortelainen, 1998). Consequently, an
exponential model has been proposed for the ageing of literature in the beginning, too
(Wallace, 1986, Price, 1963). In particular, the model of radioactive decay has been adopted.
Later on, more complex models have been developed (see, Glänzel and Schoepflin, 1995,
1999, Egghe, 1993).
Goffman and Nevill have introduced the theory of intellectual epidemics as a model of
scientific communication in 1964. According to this model the diffusion of ideas in a
population of scientists could be compared to the spreading of an influenza virus in a
population of people, causing an epidemic. This model can be used both, to describe the
spread of the disease and to predict the time when the disease reaches its peak, after which it
is presumed to decline. The advantage of the model lies in its predictive power. Goffman and
Nevill proposed that the same model could also describe the spread of information within the
scientific community. According to the model, the population can at any time be subdivided
into three groups of infected, resistant and infection sensitive persons. If a published article in
a specific topic is considered an infection, it is possible to follow the diffusion of the epidemic
by counting the number of publications per author and theoretically make a forecast of its
future. Communication between authors builds on attempts to distribute ideas aiming at
reception of disseminated information and on providing contact between infection susceptible
and already infected persons.

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Another general theory characterising processes of scientific communication is the principle
of cumulative advantage. Price formulated this in 1976 as follows.
“Success seems to breed success. A paper which has been cited many times is more
likely to be cited again than one which has been little cited. An author of many papers is
more likely to publish again than one who has been less prolific. A journal which has
been frequently consulted for some purpose is more likely to be turned to again than
one of previously infrequent use.”
Bibliometrics/Scientometrics took a sharp rise since the late sixties. In the seventies, when
data collection was often still a matter of manual work, the field bibliometrics was,
characterised by the personalities of enthusiastic researchers much in the way of a “hobby” to
later integrate interdisciplinary approaches as well as mathematical and physical models on
one side, and sociological and psychological methods on the other, not speaking of the long
tradition of library science. Later on, since the beginning of the eighties, bibliometrics could
evolve into a distinct scientific discipline with a specific research profile, several subfields
and the corresponding scientific communication structures (publication of the international
journal Scientometrics in 1979 as the first periodical specialised on bibliometric topics,
international conferences since 1983, the journal Research Evaluation since 1991).
The main reason for this development can be seen in the availability of large bibliographic
databases in machine-readable form and the fast development of computer science and
technology. This made it possible that metrics of science could be established also outside the
USA. First, license fees and expensive CPU time resulted at least in the 80s in severe
limitations but the technology of the 90s brought the breakthrough. “On-line bibliometrics”,
however, remained a dream.
The funding of large projects seems to have become the regular way of financing research in
scientometrics. From “Little Scientometrics” the field has become “Big Scientometrics”. The
publication of several comprehensive books on bibliometrics, among others by Haitun (1983),
Ravichandra Rao (1983), Bujdosó (1986), van Raan (1988), Egghe and Rousseau (1990), and
Courtial (1990), may reflect this process. The fact that bibliometric methods are already
applied to the field “bibliometrics” itself also indicates the rapid development of the
discipline.
1.4 The three “components” of present-day bibliometrics
Present-day bibliometric research is aimed at the following three main target-groups that
clearly determine topics and sub-areas of “contemporary bibliometrics”.
(i) Bibliometrics for bibliometricians (Methodology)
This is the domain of basic bibliometric research and is traditionally
funded by the usual grants. Methodological research is conducted
mainly in this domain.
(ii) Bibliometrics for scientific disciplines (Scientific information)
The researchers in scientific disciplines form the bigger, but also the
most diverse interest-group in bibliometrics. Due to their primary
scientific orientation, their interests are strongly related to their
speciality. This domain may be considered an extension of science

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information by metric means. Here we also find joint borderland
with quantitative research in information retrieval.
(iii) Bibliometrics for science policy and management (science policy)
This is the domain of research evaluation, at present the most
important topic in the field. Here the national, regional, and
institutional structures of science and their comparative presentation
are in the foreground.
Finally, we will have a look at how bibliometrics/scientometrics is linked with related fields
and application services (see Figure 1.1).
Library
Science
Information
Retrieval Scientometrics
Informetrics
Technometricss
Sociology
of Science
Research in
Services for
Librarianship
Scientific information
Science policy
Figure 1.1 Links of bibliometrics with related fields and application services

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2. THE ELEMENTS OF BIBLIOMETRIC RESEARCH AND THEIR
MATHEMATICAL BACKGROUND
According to Pritchard (1969), bibliometrics is the application of mathematical and statistical
methods to books and other media of communication. This basically comprises books,
monographs, reports, theses, papers in serials and periodicals, and nowadays also e-books and
e-journals as well as – in the broadest sense – the WEB. Nevertheless, periodicals have played
the most important part in communication in the sciences. The Philosophical Transactions of
the Royal Society and the Journal des Sçavans, that both appeared first in the year 1665, are
considered the first scientific journals.
Figure 2.1 Cover page of the Journal des Sçavans
The following figure visualises the growth of the number of scientific journals and review
journals since 1665 (according to Price, 1963).

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Figure 2.2 Growth of the number of periodicals (according to Price)
2.1 Basic concepts of elements, units and measures of bibliometric research
As mentioned above, books, monographs, reports, theses and papers in serials and periodicals
are units of bibliometric analyses. Since certain standards are postulated for such units, the
scientific paper published in refereed scientific journals proved to be the unit most suitable for
bibliometric studies. Among the common standards, we find the reviewing system, the
criterion of originality of research results, the availability of literature and the more or less
transparent rules. The scientific paper has become the basic unit of bibliometric research.
Although structural analyses of the scientific paper are conducted (for example, Mullins et al.,
1988), there are basic objects like the paper that are usually not further subdivided. These
form the elements of bibliometric analyses. Further elements besides publications, are
(co-)authors, references and citations.
Publications can be assigned to the journals in which they appeared, through the corporate
addresses of their authors to institutions or countries, references and citations to subject
categories, and so on. Under given conditions, specific sets of elements can thus be defined;
these form units. Such units are the already mentioned journals, subject categories,
institutions and countries to which elements can – not necessarily uniquely – be assigned.
Instead of this somewhat lax verbal description, a more precise definition within the
framework of appropriate mathematical models is possible, although this is hardly used in the
relevant literature. Nevertheless, we will sketch a mathematical model in a later section.
Basic measures are simple counts such as publication counts or the number of co-authors or
the number of citations received by a set of publications or of the number of given
bibliometric units. From the mathematical viewpoint, these measures can be represented by
“natural counting measures”, namely, the cardinality of the intersection or union of
bibliometric units. Figure 2.1 may just serve as an example for a basic measure, namely for
the annual change of the number of journals.

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More complex measures can be obtained as statistical functions defined on sets of
bibliometric elements and units. These measures are also called bibliometric indicators. The
fundamental demand upon bibliometric indicators is their validity, that is, we have to make
sure that we really measure what we are intending and assuming to measure. Also
reproducibility is one of the basic criteria in scientific research. Under identical conditions
research results should be reproducible in bibliometrics, too. The reproducibility of results can
only be guaranteed, if all sources, procedures and techniques are reliable and properly
documented in scientific publications.
Elements, units and measures of bibliometric research will be discussed in detail in the
following sections devoted to concrete applications.
2.2 Data sources of bibliometric research
Data sources of bibliometric/scientometric research and technology are bibliographies and
bibliographic databases. Bibliometric analyses can be conducted on the bases of any
sufficiently large publication list compiled and issued, for instance, by a scientific institution.
Nevertheless, most reliable sources are the big specialised or multidisciplinary databases that
have been first provided in printed form but later on also in electronic form (magnetic tape,
CD-ROM, on-line). Prominent specialised databases are among others Medline (life
sciences), Chemical Abstracts (chemistry-related literature and patents(!)), Inspec (physical
sciences and engineering) and Mathematical Reviews (mathematics).
The databases of the Institute for Scientific Information (ISI, Philadelphia, PA, USA), first of
all, the Science Citation Index (SCI) have become the most generally accepted basic source
for bibliometric analyses. Although, there are several objections against the journal coverage
and the data processing policy of the ISI in preparing the SCI, its unique features are basic
requirements of bibliometric technology. Among these features we mention
- Multidisciplinarity. All research fields in the life sciences, natural sciences,
mathematics and engineering are represented.
- Selectiveness. Periodicals covered by SCI are chosen on the basis of quantitative
criteria (impact measurements), and the selection is generally reinforced by expert
opinion.
- Full coverage. All papers published in periodicals covered by the SCI are recorded.
- Completeness of addresses. The addresses of all authors are indicated, allowing
analyses of scientific collaboration and the application of full publication counting
schemes.
- Bibliographical references. Together with each document their references are
processed. Redefining references as sources makes it possible to analyse citation
patterns and to construct citation indicators.
- Availability. The SCI is available as printed edition, in electronic form on magnetic
tapes, as on-line version and as CD-ROM edition. Especially the latter one gained
popularity in the nineties. The Web of Science, however, is rather a tool for traditional
information retrieval tasks.

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The SCI and the SSCI (Social Sciences Citation Index) databases also have – from the
viewpoint of bibliometric application – shortcomings. Being multidisciplinary databases they
do not provide a direct subject assignment for recorded papers. For lack of an appropriate
subject-heading system, versions of ISI’s Subject Category scheme published in annual
Science Citations Index Guides and the ISI Journal Citation Reports (JCR) are used for
bibliometric application as an indirect subject assignment of individual papers through those
journals in which they have been published. Such assignment system based on journal
classification has been developed by Narin and Pinski (see, for instance, Narin, 1976). Since
journals are often not devoted to a single topic, assignment of subject areas through journal
classification is necessarily less precise than that based on subject headings of individual
publications.
Data base availability (SCI, WoS)
The SCI database was available already in the ‘70s. The printed version can still be found in
many libraries. The main components of this edition were the following three indexes:
• Source Index
• Citation Index
• Permutation Index
Each covers the same material but indexes it differently. There is a large range of search
options the SCI and SSCI offer. The literature is indexed in different ways:
- by cited author and cited work or by cited patent (Citation Index)
- by source author (Source Index) or by source organization (Corporate Index, a section
of the source index)
- by title words (Permuterm Subject Index)
The Citation Index is the main search tool; the other indexes, however, play important
complementary roles. The Source Index can be used for author searches, and provides a full
bibliographic description of every indexed item. The Corporate Index permits searches by
organisations.
The Permuterm Subject Index (PSI) goes far beyond a conventional title-word index. The PSI
lists under each term all the other title words with which it has appeared. The refinement
enables the user to search a combination of two terms, thus increasing the specificity of the
search and decreasing the percentage of irrelevant material.
Despite of the unique features of this database, bibliometric research on the basis of the
printed edition was restricted to quite small samples. However, the same material was
provided on magnetic tapes for retrieval purposes and for scientific information. This
information service was based on weekly updates. ISI provided the annual cumulations as an
additional service for a supplementary fee. These cumulations could already be used for
computerised data processing within the framework of bibliometric studies. Data processing
on mainframe computers was, however, limited by storage, speed and above all, by the
expensive CPU-time.

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FN ISI Export Format
VR 1.0
PT Journal
AU Kostoff, RN
Braun, T
Schubert, A
Toothman, DR
Humenik, JA
TI Fullerene data mining using bibliometrics and database
tomography
SO JOURNAL OF CHEMICAL INFORMATION AND COMPUTER SCIENCES
LA English
DT Article
NR 19
SN 0095-2338
PU AMER CHEMICAL SOC
C1 Off Naval Res, 800 N Quincy St, Arlington, VA 22217 USA
Off Naval Res, Arlington, VA 22217 USA
Lorand Eotvos Univ, Inst Inorgan & Analyt Chem, H-1443 Budapest, Hungary
Hungarian Acad Sci Lib, Budapest, Hungary
RSIS Inc, Mclean, VA USA
Noesis Inc, Arlington, VA 22203 USA
AB Database tomography (DT) is a textual database analysis system
consisting of two major components: (1) algorithms for
extracting multiword phrase frequencies and phrase proximities
(physical closeness of the multiword technical phrases) from
any type of large textual database, to augment (2)
interpretative capabilities of the expert human analyst. DT was
used to derive technical intelligence from a fullerenes
database derived from the Science Citation Index and the
Engineering Compendex. Phrase frequency analysis by the
technical domain experts provided the pervasive technical
themes of the fullerenes database, and phrase proximity
analysis provided the relationships among the pervasive
technical themes. Bibliometric analysis of the fullerenes
literature supplemented the DT results with
author/journal/institution publication and citation data.
Comparisons of fullerenes results with past analyses of
similarly structured near-earth space, chemistry,
hypersonic/supersonic flow, aircraft, and ship hydrodynamics
databases are made. One important finding is that many of the
normalized bibliometric distribution functions are extremely
consistent across these diverse technical domains and could
reasonably be expected to apply to broader chemical topics than
fullerenes that span multiple structural classes. Finally,
lessons learned about integrating the technical domain experts
with the data mining tools are presented.
CR *ENG INF INC, 1999, ENG COMP
*I SCI INF, 1999, SCI CIT IND
ANWAR MA, 1997, SCIENTOMETRICS, V40, P1
BRADFORD SC, 1934, ENGINEERING, P137
GARFIELD E, 1985, J CHEM INF COMP SCI, V25, P170
KOSTOFF RN, 1995, 5440481, US
KOSTOFF RN, 1997, ADA296021 DTIC
KOSTOFF RN, 1994, COMPETITIVE INTELLIG, V5, P1
KOSTOFF RN, 1993, COMPETITIVE INTELLIG, V4, P1
KOSTOFF RN, 1998, INFORM PROCESS MANAG, V34, P69
KOSTOFF RN, 1999, J AM SOC INF SCI
KOSTOFF RN, 1997, J INFORM SCI, V23, P301
KOSTOFF RN, 1997, SCI ENG ETHICS, V3, P2
KOSTOFF RN, 1998, SCIENTOMETRICS, V43, P27
KOSTOFF RN, 1997, SCIENTOMETRICS, V40, P103
KOSTOFF RN, 1997, SCIENTOMETRICS, V39, P225
KOSTOFF RN, 1999, TECHNOVATION, V19, P593
LOTKA AJ, 1926, J WASH ACAD SCI, P16
MACROBERTS M, 1996, SCIENTOMETRICS, V36, P3
TC 11
BP 19
EP 39
PG 21
JI J. Chem. Inf. Comput. Sci.
PY 2000
PD JAN-FEB
VL 40
IS 1
GA 278YP
PI WASHINGTON
RP Kostoff RN
Off Naval Res, 800 N Quincy St, Arlington, VA 22217 USA
J9 J CHEM INFORM COMPUT SCI
PA 1155 16TH ST, NW, WASHINGTON, DC 20036 USA
UT ISI:000085016800002
ER
Figure 2.3 Complete bibliographic information about a paper by Kostoff et al. (2000)
according to the SCI Expanded

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The on-line versions of the SCI and SSCI databases, for instance, SCISEARCH and SOCIAL
SCISEARCH offered by DIMDI (Cologne), seemed to be a serious alternative to the off-line
editions also for bibliometric research (“on-line bibliometrics”. Although, DIMDI offered
many pre-bibliometric options, prices, speed and limited options were the main causes why
on-line bibliometrics remained a dream.
In the 90s, especially the CD-Editions of the three ISI databases, the SCI, SSCI and the AHCI
(Arts & Humanities Citation Index), have become very popular. Besides the standard edition,
ISI also provided a version with abstracts. The basic index can be considered an extension of
the PSI. From the second half of the 90s on, the excellent retrieval system provided with the
CD database permitted bibliometric work on any advanced PC system. Nevertheless, all data
downloaded or extracted from the CD-Edition need a careful cleaning-up. The drawback of
this popularity was the appearance of bibliometric results based on “quick-and-dirty”
searches.
The Web of Science is an online edition that combines the three ISI databases SCI expanded
(an SCI edition with broader coverage), the SSCI and the ACHI in a unique on-line database.
The SCIE covers about 5900 journals whereas the SCI covers about 3500, the SSCI covers
1700 journals and 3300 journals selectively, the ACHI finally covers more than 1100 journals
fully and about 7000 journals selectively. The WoS, in turn, is part of the more
comprehensive Web of Knowledge. The WoK comprises the above-mentioned ISI databases
as well as the Derwent Innovations Index, BIOSIS Previews, ISI Proceedings, CAB
ABSTRACTS and INSPEC bibliographic and patent databases. Figure 2.3 gives an example
for the bibliographic information provided by the WoS.
2.3 Minimum bibliographic description for paper identification
Bibliometric analyses are based on relevant information about scientific publications that can
be retrieved from the above-mentioned data sources. In the following table, most important
information used in bibliometrics is shown. This information is usually organised in
corresponding search fields.
Relevant information from bibliographic databases:
Scientific publications
1. Source identification (Journal title, PY, VOL, 1st page)
2. Names of authors
3. Corporate addresses
4. References
5. Document type
6. Title, controlled terms, keywords, abstract, subject headings
7. Acknowledgement
Although no systematic research has been done in this topic, the determination of the
minimum description of bibliographic items plays in important part in bibliometric research
and technology. This is necessary by several reasons, namely, because possible internal
identification numbers cannot be used outside the used database, to correct errors (spelling

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variances) in database fields, to be able to match items taken from different fields (reference
and source items for citation analyses) and to unify transcription standards in different
databases when information from several bibliographic databases is combined. The following
example might illustrate the necessity for finding a unified bibliographic description for paper
identification.
Example (reference items)
ZWIETERING- M -1991-APPL-ENVIRON-MICROB-V57-P1094
ZWIETERING- MH -1991- APPL-ENVIRON-MICROB -V57-P1094
ZWIETERING-MH-1991- APPLIED-ENV-MICROBIO -V57-P1094
Source: Jan-Sep 1993 cumulation of the 'Science Citation Index' (CD-Edition)
Three different variants have been found for one and the same paper in the reference strings.
According to empirical investigations, the above errors can be corrected, for instance, with the
help of the cluster-key ‘91ZWIE 571094[A]’.
2.4 Mathematical models and the “distributional” approach
Pritchard (1969) explained the term bibliometrics as “the application of mathematical and
statistical methods to books and other media of communication“. The creation and application
of mathematical models seems in this context quite obvious. Moreover, the links created by
co-authorship relations, by received and given citations form complex networks in scientific
communication that can best be described and analysed with the help of mathematical tools.
To sum up, the application of mathematical models, especially that of stochastic models and
probability distributions has several advantages, in particularly, it helps to give
1. mathematical interpretations beside the bibliometric ones,
2. understanding of complex structures such as communication networks,
3. information about statistical reliability and estimates of random errors.
2.4.1 Historical sketch of mathematical methods used in bibliometrics
As in most young emerging fields, also bibliometricians have first adopted models from other
fields to describe basic regularities they have observed. And as in most such cases, these
models proved to have limited validity. Lotka’s Law according to which authors are
producing n1/n² papers, where n1 is the number of authors having published only one article
and n the number of papers, is a typical example. Lotka has formulated as a natural law, not
taking into account important factors heavily influencing productivity. These factors will be
studies later.
A second law was formulated in the context of the growth of literature. The chart presented in
Figure 2.2 reflects a more or less exponential growth of the number of scientific journals and
of review journals. This has been generalised a general law characterising the growth of
scientific literature and of information, in general. A consequence, the growth rate is assumed

18
to be linear at any time. At lower levels of aggregation, for instance, in individual research
disciplines the growth has often be assumed to be logistic.
The exponential model of growth
In this model, the (cumulative) number of scientific publications p(t) is considered a function
of time. Moreover, the growth rate is assumed to be linear, that is, p’(t) = k·p(t), where k is a
positive real value. This simple differential equation with the initial condition p(0) = p0 leads
directly to the exponential function p(t) = p0 ·e k·t . This growth curve can be characterised by
the time td during which the value of p0 has doubled. In particular, we have td = (log 2)/k.
Consequently, td can be used as a substitute of the parameter k as follows: p(t) = p0 ·e (log 2)·t/td .
The logistic growth model
It is obvious that the growth of literature in a given topic cannot be exponential till infinity.
Beyond a certain threshold, the gradient of the linear growth function begins to decrease and
growth turns negative as “resources are exhausted”. System finally converges to a level of
saturation. This model is described by the logistic curve suggested by Pearl-Reed that can be
obtained as a solution of the following non-linear differential equation:
p’(t) = k·p(t)(b – p(t)); p∈(0, b), where k and b are a positive real values and p∈(0, b).
Under the initial condition p(0) = p0, we obtain the following solution.
p(t) = b·[1 + (b/ p0 – 1)·e –kbt] –1 , k > 0.
The following figure visualises the logistic curve that consists of three “parts”, a quasi-
exponential growth if p(t) << b, a quasi-linear growth if p(t) ~ b/2 and finally a negative
exponential growth if p(t) is close to level of saturation b.
Time (t)
p(t)
b/
2
b
exponential
quasi-linear
Figure 2.4 The logistic curve

19
The linear growth model
We just mention in passing that a linear model can approximate the growth in shorter periods.
This applied above all for the phase around the turning point in the logistic model. The
following example presents results from a “quick-and-dirty” retrieval based on the keyword
magainin. Magainin has found in the skin of certain frog species, and belongs to a broad class
of antimicrobial peptides that kill bacteria by permeabilising the cytoplasmic membrane.
Unlike conventional antibiotics, magainin does not cause resistance. The results of the
literature search in the WoS reflect almost linear growth for the 5-year period 1998-2002 with
an annual average growth rate of 41 papers (see Figure 2.5). Nevertheless, the growth rate
proved to be roughly linear (see Figure 2.6). This reflects a slow exponential growth typical
of a small emerging field. The evolution practically started from zero in 1987 and, from 1988
on, growth tripled in annual rate continuously.
0
50
100
150
200
250
300
350
400
1990 1992 1994 1996 1998 2000 2002
Publication year
Number of papers
Figure 2.5 The approximately linear growth of “magainin research” in the last five years
y = 3.056x
R2 = 0.905
0
5
10
15
20
25
30
35
40
45
50
1988 1990 1992 1994 1996 1998 2000 2002
Publication year
Growth rate
Figure 2.6 The linear annual growth rate of “magainin research”

20
Intellectual epidemics as a model of scientific communication
Goffman and Nevill have formulated their deterministic model of intellectual epidemics in
1964. Their model is based on the classical Reed-Frost model. According to this model the
diffusion of ideas in a population of scientists could be compared to the spreading of an
influenza virus in a population of people, causing an epidemic. The population can at any
time be subdivided into three groups of infected (I), resistant or immune (R) and infection
sensitive, i.e., susceptible (S) animals or persons. Goffman and Nevill have considered a
published article in a specific topic an infection.
The deterministic model proceeds from the classical Reed-Frost model, and can be described
by the following system of differential equation. First, we assume that the population is
closed, that is,
S(t) + I(t) + R(t) = N, where N is positive real constant and t is the time parameter.
For the system of differential equation, we assume:
(1) S’(t) = –βS(t)·I(t)
(2) I’(t) = βS(t)·I(t) – γI(t)
(3) R’(t) = γI(t)
In order to stabilise the epidemic model, we have to assume that
(2) I’(t) = βS(t)·I(t) – γI(t) > 0 , that is, S(t) > γ/β.
The epidemic situation occurs at a time t0 when the number of susceptible persons (S0)
exceeds the ratio γ/β. We obtain the peak of the epidemic by determining the following
extreme value. The change of the number of infected (I) and susceptible (S) persons in time
takes its maximum if [I’(t) + S’(t)]’ = [–βS(t)·I(t) + βS(t)·I(t) – γI(t)]’ = [– γI(t)]’ = 0. Since
γ ≠ 0, the right-hand side of Eq (2) must vanish, i.e., S(t) = γ/β. This contradicts the condition
that the epidemic situation occurs if S exceeds this value. Consequently, we have to assume
an open population, that is, we have to assume that N is a increasing function of time.
According to Goffman, an open population has to be assumed since sensitive and infected
persons have to be continuously replaced by persons entering the system. Here, we just refer
to a model by Schubert and Glänzel introduced in 1983 to describe stationary publication
processes. This model will be discussed somewhat later, in the context of stochastic
processes.
In the case of the open population, the condition for reaching the peak can be derived
analogously to the previous case. In particular, we obtain S(t) + I(t) = const or R’(t) = const as
sufficient conditions for reaching the peak.
2.4.2 Basic postulates and the “axiomatic approach” to bibliometrics
We can formulate the following basic postulates or even axioms without which bibliometric
measures cannot properly be defined and used.

21
1. A paper receives at one time at most one citation.
2. An author publishes only one article at one time.
3. A paper does not receive citations prior to it its publication
4. The citation link between two papers is unique
The publication process from the bibliometric viewpoint
(at time t and in the period T = [s, t])
Authors Papers
Co-authors
F t
Authors Papers
Co-authors
F T
t 2
t 1t 3
Figure 2.7 The relationship between bibliometric elements and units in terms
of their mathematical interpretation (author–publication links)

22
The first two postulates are necessary to define mappings and allow the application of point
processes. Sometimes occurs, however, that a paper receives more than one citation in the
same issue of a journal, that is, by papers that appear at the same time. This can be solved by
using an infinitesimal number ε > 0, so that the paper is, for instant, cited by the publications
of the same issue at time t, t + ε, t + 2ε, etc. The case that an author has more than one paper
in one and the same issue of a journal can be treated analogously.
The second postulate is straightforward and the third one is necessary to make quantification
of citation impact possible. The database producer normally guarantees uniqueness of citation
links.
The citation process from the bibliometric viewpoint
(at time t and in the period T = [s, t])
Y t
Source papers Citing papers
References
References
Y T
t 2
t 1t 3
Source papers Citing papers
Figure 2.8 The relationship between bibliometric elements and units in terms
of their mathematical interpretation (citations links)

23
Figures 2.7 and 2.8 visualise the formalism of mathematical interpretation of relationship
between bibliometric elements. In the first case, the mapping Ft (for each time t) is describes
an authorship. t is the publication date. The observation period T = [s, t] is called publication
period. FT then forms the publication process of an author. The complete origin Ft–1 of a given
publications is the set of its co-authors, in particular, if we denote the set of authors by A and
that of papers by B, then we have for each element b ∈ B: Ft–1(b) = {a ∈ A: Ft(b) = b}.
In the second case, the mapping Yt (for each time t) describes a citation. t is the publication
date of the citing paper. The observation period T = [s, t] is called citation window. YT then
forms the citation process of a paper. The complete origin Yt–1 of a given publications is the
set of its references, in particular, if we denote the set of source papers by A and that of citing
papers by B, then we have for each element b ∈ B: Yt–1(b) = {a ∈ A: Yt(b) = b}.
2.4.3 Deterministic models of productivity and citation processes
Publication activity as a measure of ‘scientific productivity’
As already mentioned in the context of the epidemic model according to Goffman, an open
population has to be assumed since susceptible and infected persons have to be continuously
replaced by persons entering the system. The model by Schubert and Glänzel introduced in
1983 describes similar publication processes. This model assumes three groups in the
population, namely, 1. those who entering the system, 2. those who are staying in the system
and 3. those who are leaving it. The system can be described as follows.
Consider an infinite array of units indexed in succession by the non-negative integers. The
content of the i-th unit is denoted by xi, the (finite) content of all units by x. Then the fraction
yi=xi/x (i ≥ 0) expresses the share of elements contained by the i-th cell. The change of
content is postulated to obey the following rules.
(i) Substance may enter the system from the external environment through 0-th unit at a
rate s;
(ii) substance may be transferred unidirectionally from the i-th unit to the (i+1)-th one at
a rate fi (i ∈ N0);
(iii) substance may leak out from the i-th unit into the external environment at a rate gi
(i ∈ N0).
The next step towards a stochastic model is to interpret the above ratios yi as the (classical)
probability with which an element is contained by the i-th unit. The stochastic process is then
formed by the change of the content of the units, i.e., by the change of papers published by the
authors who have entered the system. X(t) denotes the (random) number of published papers,
P(X(t) = i) = yi the probability that an author in the system has published exactly i papers in
the period t. Finally, the stochastic model itself is obtained if X(t) is considered the
publication activity process of an arbitrary author, and P(X(t) = i) = yi is the probability that
he/she has published i papers in the interval (0, t). Figure 2.9 visualises the scheme of
substance flow of this process.

24
Figure 2.9 Scheme of substance flow in the Waring process
Now, using the above notations, we can give a mathematical formulation for the equations of
change in the system.
x0'(t) = s(t) - f0(t) - g0(t) ,
.
. (1)
.
xi'(t) = fi-1(t) - fi(t) - gi(t) , (i > 0).
Here and in the followings, the prime (') denotes time derivatives.
According to Schubert and Glänzel, the following particular forms of the above rate terms are
used:
s = σ⋅x , (2)
fi = (a + b
⋅
i)⋅xi ; (i ≥ 0) , (3)
gi = γ⋅xi ; (i ≥ 0) , (4)
where σ, a, b and γ are non-negative real values. Since x'(t) = Σxi' = (s – Σgi) = (σ – γ)⋅x
(cf. Eq. (1)), the distribution of the substance over the units during time t can be obtained as a
solution of the following system of first order linear differential equations:
y0'(t) = σ - (a + σ)⋅y0
.
. (5)
.
yi'(t) = (a + b
⋅
(i-1))⋅yi-1 - (a + b
⋅
i + σ)⋅yi ; i > 0 ,
with the initial conditions
yi
i()010
0
==



if
otherwise.

25
For the entire population we can derive x(t) = x(0)⋅exp((σ-γ)⋅t), i.e., the system is
asymptotically time-invariant (stationary) if σ = γ, otherwise, if σ > γ or σ < γ , it
exponentially grows or decays, respectively. The general solution of the above system of
differential equations is
yt be ab abi
aab abi
iij
j
i
abi t
() ( )...( ( ))
( )( )...( )
()
=+
++−
+++ ++
=
−+⋅+
∑
0
1
σ
σ
σσ σ
(6)
where the coefficients bij are determined by the initial conditions. Finally, if σ = γ is assumed,
the above process has a non-degenerated limit distribution, which is a Waring distribution
with parameters N = a/b and α = σ/b .
The following three special cases should be mentioned.
1. a = 2 ⇒ Price distribution (Glänzel & Schubert, 1985)
2. N = 1 ⇒ Yule distribution
3. b = 0 ⇒ Geometric distribution
Derrek de Solla Price distinguished the following categories of authors: newcomers,
continuants, transients and terminators. Within the framework of this model, s represents the
group of newcomers, gi terminators, g1 transients and substance remaining in the system
represents the group of continuants.
We just mention in passing that the two cases of the epidemic model according to Goffman
are obtained if σ = γ, or σ > γ, respectively.
Citation impact as a measure of reception of information
The following model introduced by Glänzel/Schubert/Schoepflin (1994/95) uses a negative
binomial process (a special case of a non-homogeneous birth-process) to describe the change
of citation impact in time and for the ageing of scientific literature.
Consider now the same array of units as in the case of publication activity. In contrast to the
above model we now assume that the system is completely isolated from external influences,
i.e., no substance enters or leaves the system. Therefore only rule (ii) of the preceding
paragraph remains valid. Hence x(t) = x(0) follows immediately, where, of course, x(0) > 0 is
assumed. The special assumption x(0) = 1 does not mean any restriction of generality. Now
we reformulate Eqs (2)-(4):
σ = 0 , (2')
fi = (a + bi)⋅xi ; a(t)/b(t) = const ( > 0) , (3')
gi = 0 ; (i ≥ 0) . (4')
The subsidiary condition to Eq. (3') says that the process is non-homogeneous, i.e., the
substance flow may depend on the time elapsed. The proportionality coefficient in the
subsidiary condition is denoted by N , i.e., a(t) = N·b(t). Figure 2.10 shows the scheme of
substance flow of this process.

26
Figure 2.10 Scheme of substance flow in the non-homogeneous birth process
By analogy to the Waring model we have
y0'(t) = -N
⋅
y0
⋅
b(t)
y1'(t) = (N
⋅
y0(t) - (N+1)y1(t))⋅b(t)
.
. (5')
.
yi'(t) = ((N+i-1)⋅yi-1(t) - (N+i)yi(t))⋅b(t) ,
with the same initial conditions as above.
Publication-activity dynamics is basically reflected by the distribution P(X(t) = i) of the
process. Special conditional probabilities, the so-called transition probabilities, however,
permit a much deeper insight into scientific productivity processes. In our case, for example,
the probability that an author publishes j papers during t years, provided he/she has published
already i papers during s years, is called transition probability (i ≤ j, s < t). These probabilities
reflect the influence of an initial period on the further publication activity. In particular, the
probability that at time t the substance is in the k-th unit, provided it was in the i-th one at
time s, is denoted by pik(s,t) (k ≥ i). With the transition rules as above, we can write (see e.g.,
Karlin and Taylor, 1975)
∂pik(s,t) / ∂t = {(N+k-1)pi,k-1(s,t) - (N+k)pik(s,t)}⋅b(t) ; k > i (7)
The initial conditions are
pss ki
ik (,)==



1
0
if
otherwise.
For simplicity, let X(t) denote the (random) index of that unit in which the substance is at time
t. Then the following distribution can be obtained from the first system of differential
equations by successive integration
,)1(
1
)())(( )()( ktrNtr
kee
k
kN
tyktXP −− −







−+
=== (8)

27
where ∫
=
t
uubtr
0
d)()( , i.e., the distribution of substance over the units is negative binomial at
any time. Analogously, the second system of differential equations results in
pst PXt Xs jXs i Nij
jee
ik
rt rs N i rt rs j
*(() ())( ) (() ())
(,) ( () () () ) ( ) ,=−===
++ −




⋅−
−− + −−
11 (9)
where pik*(s,t) = pij(s,t) with i = k-j
≥
0 . Eq. (9) can be reformulated verbally as follows. The
substance flow during the time period t-s has a negative binomial distribution with parameters
exp(-r(t)+r(s)) and N+j, where j is the index of the unit which was reach by the substance at
time s.
The mean value function of the process is defined as the regression function of X(s, t) on
X = i, namely,
Mi(s,t) = E(X(t)-X(s)|X(s)=i) . (10)
This function will play an important role in the applications. Under the above conditions we
have
Mi(s,t) = (N+i) (exp(r(t)-r(s)) - 1) ; i ≥ 0, t ≥ s (11)
and
M(s,t) = E(X(t)-X(s)) = N
⋅
(exp(r(t))-exp(r(s))) (12)
Eq. (12) reflects the non-homogeneity of the process, i.e., for example, M(s,s+h) ≠ M(t,t+h) if
s ≠ t (h > 0). Non-homogeneity is an important property of citation processes. The process has
a non-degenerated or degenerated limit distribution according as lim r(t) < +∞ or
lim r(t) = +∞ , respectively.
A model of ‘synchronous’ and the ‘diachronous’ citation processes and the ageing of
literature
In citation studies, two basis approaches have been distinguished, namely, the diachronous
and the synchronous model. The diachronous approach is concerned with the use of a given
set of publications in successive years, whereas synchronous studies proceed from the present
to the past. Consequently, we can derive two types of different citation processes, particularly,
the ‘synchronous’ and the ‘diachronous’ process. In some recent publications, Burrell (2001,
2002) has used the terms retrospective and prospective citation studies, where the terms
‘retrospective’ and ‘prospective’ are practically synonyms for ‘synchronous’ and
‘diachronous’, respectively.
First Wallace (1986) has studied ageing of scientific literature. In particular, he analysed, the
relationship between journal productivity and obsolescence, and assumed an exponential
distribution. In his model, ageing analogously is related to the radioactive decay characterised
by the “half-life” being the median of the distribution. Wallace’s study is based on the
synchronous approach, that is, he analysed the age of reference literature. From the pragmatic

28
point of view, on can say that synchronous analyses are easier to conduct since it does not
require the observation of citations in a quite large citation window of ten, fifteen or even
more years. Nevertheless, the synchronous approach cannot serve as a substitute for
diachronous studies since the two approaches shed light on quite different aspects of citation
processes, in general, and of ageing, in particular.
Although most synchronous (retrospective) ageing studies are based on the analysis of
references in selected papers, synchronous studies can also be concerned with the analysis of
citation received by publication sets. In both cases, the citation window is fixed and the
publication period is variable. Thus, both the Citing and the Cited Journal Package in the
annual up-dates of the Journal Citation Reports (JCR) have, for instance, to be considered
synchronous citation approaches.
The terms synchronous/diachronous are nowadays also used in a more general context of
citation analyses that are not directly related to ageing. Ingwerson et al. (2000, 2001) have
introduced a distinction between synchronous and diachronous impact measures for scientific
journals. According to their approach, the ‘Garfield Impact Factor’ produced by the Institute
for Scientific Information is a synchronous Impact Factor as it the citation year is fixed and
the two-year publication period lying in the “past”. In the above-mentioned studies,
Ingwersen et al. have given a methodological discussion why the ‘diachronous’ approach
should be preferred to the ‘synchronous’ one. The fact that only diachronous impact measures
can be calculated for non-serials is one of the advantages. The journal impact measures built
since 1995 at LHAS in Hungary and at RASCI in Germany may serve as examples for such
diachronous impact measures; here the publication year is fixed and citations are counted in a
three-year observation period, namely, in the year of publication and the two subsequent years
(for instance, Glänzel, 1996).
In the following, we will give a brief overview of ageing from the perspective of technical
reliability visualising the different aspects that can be analysed by the two approaches. In the
subsequent section a stochastic model will be given showing that one and the same model can
be used to describe both diachronous (prospective) and synchronous (retrospective)
perspectives of citation processes.
2.4.4 The stochastic approach to bibliometrics
Diachronous and synchronous ageing studies in the context of technical reliability
Statistical functions provided by synchronous studies depend on too many factors to be
uniquely interpreted in terms of ageing alone. In order to illustrate this effect we will refer to a
simple model adopted from technical reliability processes (see, for example, Watson and
Wells, 1961, Gupta, 1981). This may help to interpretation the two approaches. It should be
stressed at once that the technical reliability model can not be applied to explain information
processes, moreover, basic principles such as lack of memory property (technical reliability)
and cumulative advantage principle (bibliometric processes) can be considered almost
diametrical. The basic questions concerning synchronous and diachronous approach to
obsolescence are, however, very similar in informetrics and technical reliability.
Within the framework of technical reliability analyses, function and lifetime of a system, a
machine, a device or equipment is studied. The equipment may, for example, consist of
machines in factories or of automobiles, but it might also be a simple device such as a rubber
tyre or an ordinary electric switch. The usual definition of reliability of a system or a device is
the probability that it will give satisfactory performance of its intended function for a

29
specified period under specific operating conditions. Using a set of systems or devices
assumed to have identical parameters, reliability measures then give information about the
following.
1. The probability that a given system or device will operate for a specific time
2. The number of failures that will occur over a specific period of time
3. The average time between failures
4. The expected lifetime of a system, machine or device provided it works already for a
given period without failure
Burrell (2002) has already pointed to the fact that it might perhaps be unfortunate to think of
citation as a “failure”, however, this approach allows adopting model and terminology of
technical reliability. Moreover, if ageing is measured by the number of received citations and
the time elapsing between successive citations, the assumed “analogy” between failures in
technical reliability and citations in the informetric ageing model does not at all seem to be
absurd.
Lifetime is usually interpreted whether as time until failure or as time until death or
destruction. In more general terms one could also consider ‘lifetime’ the time during which a
system is or can be used; beyond this time it will not perform its intended function anymore.
This definition can straightaway be applied to information science and bibliometrics as well.
In particular, if citations are interpreted as one important form of use of scientific information
within the framework of documented science communication (Glänzel and Schoepflin, 1999)
then “technical reliability” of a scientific paper expresses the performance of its intended
function, namely, that it is read and that it is has an impact on scientific research. The latter
one can at least in part be measured by citations. Lifetime can consequently be interpreted as
the period until it is not cited anymore. Analogously to a brand-new device that is not
operating satisfactorily, a paper that is never cited can be considered not to give satisfactory
performance of its intended function already when it was published.
The concept of technical reliability implies a diachronous approach. A device is produced, it
is operating, and failures and finally death or destruction is observed. Despite the different
background and the different interpretation of the diachronous and synchronous approach, it
might, however, occur that the mathematical laws derived from the two approaches are very
similar, so that the same formula could be used in both cases. In order to disprove this
possible assumption, we will give a simple empirical evidence for the necessary distinction
between the diachronous and the synchronous approach to ageing of scientific literature. The
following example may just serve to visualise why diachronous bibliometric processes are not
merely the “reflection” of the corresponding synchronous process. In order to show this, we
have selected three journals representing three different subject fields, particularly, the
journals Cell (Biosciences), JACS (Chemistry) and Zeitschrift für Wahrscheinlichkeitstheorie
und verwandte Gebiete (since 1986: Probability Theory and Related Fields) (Mathematics).
Figure 2.11 presents the two lifetime curves simultaneously.

30
0%
5%
10%
15%
20%
25%
-20 -15 -10 -5 0 5 10 15 20
Years prior/after publication
Relative frequentie of references/citations
Cell
0%
5%
10%
15%
20%
25%
-20 -15 -10 -5 0 5 10 15 20
Years prior/after publication
Relative frequentie of references/citations
JACS
0%
5%
10%
15%
20%
25%
-20 -15 -10 -5 0 5 10 15 20
Years prior/after publication
Relative frequentie of references/citations
Z Wahrscheinlichkeit
Figure 2.11 Relative frequency of references and citations for three selected journals in 1980
(top: CELL, centre: JACS, bottom: Z Wahrscheinlichkeit)

31
In what follows, a concise introduction into diachronous/synchronous citation processes will
be given. It is based on a more general stochastic action-reaction models introduced by
Glänzel (1983). In order to do without an excessive use of mathematical formalism, a verbal
description of the rudiments is given. Nevertheless, the use of equations and formulae later on
in the text will not completely be avoidable. The citation process will be defined as a
diachronous process.
1. The basic idea of an action-reaction model is the introduction of stochastic processes
through timing-functions defined on two discrete finite subsets in the original
probability space. The two subsets will be denoted by A and A’, where these subsets
need not be disjoint; they may even be identical. The elements of these sets are in the
present paper assumed to be publications. The probability measure is defined as an
elementary measure on the basis of a counting measure φ.
2. There are two subsets M and N of R (the reel axis) or Z (the set of integers),
depending on whether a continuous or discrete time model is used. Without loss of
generality we assume that M ⊆ N. These sets represent the time-parameter. In
particular, the mappings ν: A → M and µ: A’ → N are called timing-functions
indicating when an event has happened, that is, in the present case, when a paper is
published. In the following, time is assumed to be discrete, that is, M, N ⊆ Z. The
elements of these sets can, instance, be the publication years of scientific papers.
3. The mapping τ: A’ → A describes the link between citing (A’) and cited papers (A).
Using an a bit lax formulation, one can define its “inverse” mapping in the following
manner. Let A’N denote the set {A’tn,a : tn ∈ N, a’ ∈ A}, where
A’tn,a = {a’ ∈ A’: µ(a’) = tn ∧ τ(a’) = a}. In verbal terms, A’N is the set of papers
published in the period N and citing papers of the set A. Then the following mapping
is uniquely defined: Λ: N × A → A’N , where Λ(tn , a) = A’tn,a . The mapping
X* = φ ° Λ then defines the increments of a stochastic process, namely the number of
citations received by a paper a at time tn . The process X then is the number of
citations received in the period t ≤ tn , that is, X(tn) = Σt≤tn X*(t) . X: A × N → IN is an
appropriate stochastic process that can be used as a model for diachronous citation
process.
4. Random selection. It is clear that in the above paragraphs a stochastic process Xs is
defined for each s ∈ M. The complete set of processes defined this way is
X = {Xs}s∈M . Then the measurable mapping ν: A → M defines a random selection of
processes from the set X. Without loss of generality we can extend the definitions of
the processes by putting N = M and defining Xs(t) ≡ 0 for all t < s. In the discrete case,
a process Xs(tn) can then be selected with probability ps = P(ν = s) for all s ∈ M = N.
An alternative presentation of probability measures based on these processes is
possible through the use of conditional distributions, where the condition is given by
the selection of publication period, that is, for instance, E Xs(t) = E(X(t) | {ν = s}).
5. The appropriate synchronous process can now readily be derived from the
diachronous one by fixing t and through random selection from the corresponding set

32
of increments X
* = {Xs*}s∈M. Random selection from the set X, or from X* with
variable t, respectively, will result in hybrid diachronous-synchronous processes.
We give three examples for functions that can be used to measure ageing properties of the
process. First, we can assume that if inf sup N = ∞ and the process is convergent, that is,
Xs(tn) converges to a non-degenerate random variable Xs(∞) with probability 1 for each
s ∈ M. We can further more assume that the sequence is uniformly integrable. Under these
conditions, which are quite natural for citation processes, we can define the following
measures.
The mean-value function is the simplest of these measures. It is defined as the mean value of
E Xs(tn) for each s ∈ M at any given time tn. Its basic properties are obvious from the
definition and the above assumptions: E Xs(tn) is a non-negative, increasing function and
E Xs(tn) → E Xs(∞) < ∞.
Hence we can define the second function, the life-time function of the process (see Glänzel,
1983). In particular, it takes the following form:
P(µ ≤ tn) = E Xs(tn)
E Xs(∞) .
This life-time function can also be called life-time distribution, since 0 ≤ P(µ ≤ tn) ≤ 1 and
lim tn→∞ P(µ ≤ tn) = 1. This distribution has already been used, for instance, in the studies by
Glänzel and Schoepflin, 1994 and Burrell, 2002.
One possibility to define an obsolescence function of the process Xs (s ∈ M) as the third
function is given in the following (see Glänzel and Schoepflin, 1994). We say an element in
the model is obsolete at time tn if it will not be cited at any time t’ > tn. The probability Hs(tn)
of becoming obsolete is called obsolescence function of the process and is defined as
Hs(tn) = P(Xs(∞) – Xs(tn) = 0) .
Hs is an increasing function on N. Although 0 ≤ Hs(tn) ≤ 1 and obviously Hs(∞) = 1, H is in
most cases not a distribution function since Hs(s) = P(Xs(∞) = 0) and P(Xs(∞) = 0) might be
positive.
Citation Distributions and Statistical Reliability of Comparisons
First, we give an example for citation distributions of scientific journals without proposing
any particular model. Citation distributions are discrete and often very skewed. The following
figure (Fig. 2.12) presents the distribution of citation over papers published in the journals
Angewandte Chemie (Intern. Edition) and JACS in 1995/96. Citations have been counted in
the period 1995-1997 for papers published in 1995 and in 1996-1998 for papers published in
1996.

33
0%
2%
4%
6%
8%
10%
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50+
ACH (9.37)
JACS (11.02)
Figure 2.12 Distribution of citation over papers published in the journals Angewandte
Chemie (Intern. Edition) and JACS in 1995/96
Figure 2.13 shows the empirical distribution of three samples and their fit on the basis of the
above-mentioned model by Glänzel, Schubert and Schoepflin. Again, citations have been
counted in the period 1995-1997 for papers published in 1995 and in 1996-1998 for papers
published in 1996. The tree samples represent three different types of citation distributions.
The first one (The Lancet) is extremely skewed and highly polarised. In a later section, we
will see that that is in part due to the high share of Letters to the editor published in this
journal. The shape of the distribution of the second sample (the field of neuroscience) is less
skewed and less polarised. The last example, that of the journal Nature reflects the most
advantageous situation.
It is a misbelief that the use of mean values is not justified in case of discrete, skewed
distributions. Sample means have under certain conditions a N(m, σ) distribution where m is
the expectation of the underlying (discrete) distribution and σ depends only on the standard
deviation of the distribution and the sample size. In this context, the Impact Factor and related
measures based on other publication periods and citation windows can be interpreted as
sample means. Then the Mean Citation Rate
x
of a journal is an unbiased estimate of the
expectation of the underlying random variable X. That is, we have )()( XExE =and
nXDxD /)()( 22 =, where n is the number of source items of the journal J in the publication
period. )(xD is the standard error of
x
. It can be used as a basis for comparisons with the
impact of other journals and allows to decide whether the deviation of the impact of a journal
from that of another one is significant or not (see Schubert and Glänzel, 1983). The following
example might illustrate this.

34
0
20
40
60
80
100
120
0 2 4 6 8 101214161820222426283032 3436384042444648
Citations
Frequency
Lancet
Observed
Estimated
N = 23.35
P = 0.75
0
20
40
60
80
100
120
024681012141618202224262830323436384042444648
Citations
Frequency
Neuroscience
Observed
Estimated
N = 3.33
P = 2.04
0
20
40
60
80
100
120
0 2 4 6 8 101214161820222426283032 3436384042444648
Citations
Frequency
Nature
Observed
Estimated
N = 46.03
P = 1.07
Figure 2.13 Distribution of citation over papers and their fits on the basis of
a negative-binomial distribution

35
Example: Compare the mean citation rate of Austrian and Hungarian mathematical papers
published in 1978/79 (citations counted in 1980).
Austria: xA = 0.248 D(xA) = 0.073
Hungary: xH = 0.226 D(xH) = 0.045
We have
257.0
045.0073.0
226.0248.0
)()( 2222 =
+
−
=
+
−
=
HA
HA
xDxD
xx
w.
Since |w| < 1.96 = wp (p = 0.95) the deviation is not significant at a confidence level of 0.95.
In this context, we have to mention that Haitun (1989) rejects the application of traditional
mathematical statistics to bibliometrics referring to non-Gaussian nature of bibliometric data.
However, his approach remained controversial.
Using stochastic models, further important questions can be answered, for instance, in how
far the succession of citations received can be described by mathematical laws (e.g., Glänzel,
1992a, Burrell, 2001). Especially, the first-citation distribution is of particular interest. This
has been studied by Schubert and Glänzel (1986), Glänzel (1991), Rousseau (1994), Egghe
(2000) and Burrell (2001). Schubert and Glänzel (1986) have used first-citation to measure
the speed of reception of scientific results.

36
3. INDICATORS OF PUBLICATION ACTIVITY
3.1 Counting schemes and main levels of aggregation
Publication activity is expressed by the number of papers published by a selected unit in a
given time.
Counting schemes are the method according to which publications are to be assigned to the
contributing units. In particular, three “counting schemes” are used for publications.
1. The fractional counting scheme, that is, if n units (authors, institutions, countries,
etc.) have contributed to the paper in question, each contributing unit takes the value
1/n for this paper (for instance, applied by CHI Research Inc., Haddon Heights, NJ,
USA)
2. The first address count, i.e., a paper is assigned to one unit only, on the basis of the
first address in the address list of a paper as included in the database (for instance,
used by Information Science and Scientometrics Research Unit (ISSRU), Budapest,
Hungary in the 80s).
3. The full or integer counting scheme assigns a co-publication fully to each
contributing unit (applied by the Centre for Science and Technology Studies (CWTS),
Leiden, Netherlands, in the 90s also by ISSRU and the Research Association for
Science Communication and Information e. V. (RASCI), Germany).
Due to intensifying scientific collaboration, the use of the first or correspondence address
proved not an appropriate scheme for the 90s. Although fractional counts are partially
additive, i.e., data from a lower level of aggregation can be summed up a higher one or the
total, this scheme proved highly problematic if the fractionation criterion (institutional,
regional, national fractionation) is not documented, and data are taken out of their context.
This can be illustrated by the following example presented in figure 3.1. This paper has nine
co-authors working at three different institutions that are located in two different countries.
Applying fractional counting to the example in Figure 3.1, each co-author contributes with a
“share” of 0.111, each institution involved with 0.333 and each country with 0.500. Since the
authors are not employees of the same institutions and the corporate addresses are in two
different countries, fractional counts cannot be summed up among the different levels of
aggregation. Figure 3.2 visualises what happens if subsets do not form partitions and different
levels of aggregations (units) are represented by systems of overlapping subsets. The same
formalism representing author-publication links is used as in Figure 2.7.
SCI CDE with Abstracts (Jan 93 - Jul 93) (D4.0)
Authors: Prassides-K Kroto-HW Taylor-R Walton-DRM David-WIF Tomkinson-J Haddon-RC
Rosseinsky-MJ Murphy-DW
Title: Fullerenes and Fullerides in the Solid-State - Neutron-Scattering Studies
Full source: CARBON 1992, Vol 30, Iss 8, pp 1277-1286
Addresses: UNIV-SUSSEX, SCH CHEM & MOLEC SCI, BRIGHTON BN1-9QJ, E-SUSSEX, ENGLAND
RUTHERFORD-APPLETON-LAB, DIDCOT OX11-0QX, OXON, ENGLAND
AT&T-BELL-LABS, MURRAY-HILL, NJ 07974, USA
Figure 3.1 Bibliographic data of the example for different fractional counting
according to different levels of aggregation

37
Ft
Authors Papers
Institution
Country
Figure 3.2 Example for different levels of aggregations represented
by overlapping systems of subsets
As a consequence of this effect, comprehensive studies including analysis of collaboration
patterns, comparisons of relative publication activity and relative citation impact require
full-address counts. Moreover, each level of aggregation has its own bibliometric standards.
Users should therefore take into consideration that data sets designed for studies at different
levels of aggregation might be incompatible (see Glänzel, 1996).
Levels of aggregation in bibliometric research
From the viewpoint of bibliometric methodology, the distinction between three levels of
aggregations is important. Each level of aggregation requires its own methodological and
technological approach.
Micro level: Publication output of individuals and research groups
Meso level: Publication output of institutions; studies of scientific journals
Macro level: Publication output of regions and countries; supra-national aggregations
There are various reasons for this necessary distinction, among others, the mathematical-
statistical background, the precision of retrieval and cleaning-up of data, different counting
schemes, different meaning of bibliometric conceptions (e.g., self-citations), non-additivity of
bibliometric data (because of multiple assignment).

38
3.2 Problems of subject assignment
Subject assignment is necessary to describe publication activity in given subject areas or sub-
fields. Publications can be assigned to subjects through
a) subject codes or subject headings,
b) key-words or
c) journals classification.
Subject assignment is largely determined by the bibliographic database used for bibliometric
application. From the viewpoint of the given practical purpose, two different basic schemes
are used: Hierarchic and fine-structured classification systems used in information retrieval
and more “robust” schemes emphasising science organisation aspects and science policy
needs. Specialised databases such as INSPEC (PACS codes) or Mathematical Reviews (MSC
codes) allow retrieval at very low levels of classifications, for very specialised topics. Figure
3.3 illustrates the hierarchical structure of the MSC-code system of the database
“Mathematical Reviews“ defining the topic “Characteristic functions; other transforms” as
subtopic of “Distribution theory” which is in turn a sub-discipline of the subject “Probability
theory and stochastic processes”.
51-xx Geometry
52-xx Convex and discrete geometry
53-xx Differential geometry
54-xx General topology
55-xx Algebraic topology
57-xx Manifolds and cell complexes
58-xx Global analysis, analysis on manifolds
60-xx Probability theory and stochastic processes
62-xx Statistics
65-xx Numerical analysis
68-xx Computer science
60Axx Foundations of probability theory
60Bxx Probability theory on algebraic and topological structures
60C05 Combinatorial probability
60D05 Geometric probability, stochastic geometry, random sets
60Exx Distribution theory
60Fxx Limit theorems
60Gxx Stochastic processes
60Hxx Stochastic analysis
60Jxx Markov processes
60Kxx Special processes
60E05 Distributions: general theory
60E07 Infinitely divisible distributions; stable distributions
60E10 Characteristic functions; other transforms
60E15 Inequalities; stochastic orderings
60E99 None of the above, but in this section
Figure 3.3 Example for the hierarchical structure of the MSC-code system
(subject 60: Probability theory)

39
“Reliability” and “precision” of this scheme are excellent. Papers are assigned individually,
on the basis of the authors’ classification and corrections by reviewers. Nevertheless, subject
classification (especially at lower hierarchical levels) is not unique as multiple assignments
are allowed (MSC Primary/Secondary). Using the above example, an article might, for
instance, be concerned with characteristic functions or other transforms of stable distributions
(60E10 and 60E07).
As already mentioned, ISI databases do unfortunately, not provide a direct subject assignment
for indexed papers. The multidisciplinarity of the database can be considered the main reason
for lacking paper-based subject classification. The annual Science Citations Index Guides and
the ISI Journal Citation Reports (JCR), however, contain regularly updated lists of journals
assigned to one or more subfields (ISI Subject Categories) each. For lack of an appropriate
subject-heading system, more or less modified versions of this Subject Category scheme are
often used in bibliometric studies, too, namely as an indirect subject assignment of individual
papers through those journals in which they have been published. Such assignment system
based on journal classification has been developed among others by Narin and Pinski (see, for
instance, Narin, 1976). Taking into consideration that journals are often not devoted to a
single topic, the delimitation of subject areas based on journal assignment is necessarily less
precise than that based on subject headings of individual publications as, for instance, in the
MSC-code system. The specialisation of journals in Condensed Matter Physics (CMP) may
just serve as an example. The extent of specialisation here ranges from Act Chryst C which is
devoted to one single subject to Phys Rev L publishing papers in all the 17 CMP subdivisions
according to the Physics Abstracts database (see Todorov and Glänzel, 1990). Since the
above-mentioned approach by Narin and Pinski, other institutions have attempted to create
their own hierarchical journal-based classification systems. In Europe, main three schemes
developed at ISSRU (Budapest), ISI (Karlsruhe) and CWTS (Leiden) were in use. All these
schemes are based on ISI journal assignment. Besides “general” journals that can at least be
assigned to one of the major science fields like physics or chemistry, there are the big
multidisciplinary journals such as Nature, Science and P NAS US publishing papers from
almost all disciplines. A journal assignment would here obviously fail. The same applies to
many selectively covered journals in the SSCI and AHCI. Selectively covered journals are
often represented by one or two papers that are indexed because all other papers published in
the same issue are not relevant for the corresponding database. In order to overcome this
problem, several methods have been developed to assign papers published in such journals
individually. Among those, the following two approaches deserve to be mentioned. 1. using
cognitive words, for instance, from the address field (de Bruin and Moed, 1993) and 2.
analysing the reference literature of those papers (for instance, Glänzel et al., 1999).
Figure 3.3 may serve as an example for a classification scheme developed for bibliometrics
purposes on the basis of journal assignment and applying an individual scheme based on
reference literature to papers published in multidisciplinary journals. The scheme can be
characterised as a two-level hierarchical system for subject fields and subfields and keeping
the subject categories still as the third and lowest level. The example presented in Figure 3.3
shows the subject category “gerontology” at a category of the subfield “age & gender related
medicine” within the field “non-internal medicine”. This type of classification schemes
proved to be robust enough for policy-relevant bibliometric applications.

40
1. AGRICULTURE & ENVIRONMENT
2. BIOLOGY (ORGANISMIC & SUPRAORGANISMIC LEVEL)
3. BIOSCIENCES (GENERAL, CELLULAR & SUBCELLULAR BIOLOGY; GENETICS)
4. BIOMEDICAL RESEARCH
5. CLINICAL AND EXPERIMENTAL MEDICINE I (GENERAL & INTERNAL MEDICINE)
6. CLINICAL AND EXPERIMENTAL MEDICINE II (NON-INTERNAL MEDICINE SPECIALTIES)
7. NEUROSCIENCE & BEHAVIOR
M1 age & gender related medicine
M2 dentistry
M3 dermatology/urogenital system
M4 ophthalmology/otolaryngology
M5 paramedicine
M6 psychiatry & neurology
M7 radiology & nuclear medicine
M8 rheumatology/orthopedics
M9 surgery
AZ ANDROLOGY
LI GERIATRICS & GERONTOLOGY
LJ GERONTOLOGY
SD OBSTETRICS & GYNECOLOGY
TQ PEDIATRICS
Figure 3.3 Example for the hierarchical structure of a scheme based on ISI categories
(Subject field: non-internal medicine)
As already mentioned earlier, assignment to units (for instance, on the basis of addresses) is
often not unique. The same applies to subject classification. A problem arises if data have to
be aggregated or disaggregated from one level of aggregation to another one. Whenever
publications cannot be uniquely assigned to one single category aggregation or disaggregation
is problematic or may lead to invalid results. We have to stress again that bibliometric
indicators are not additive over (sub-)fields or most other units of aggregation. Alone journals
always form disjoint sets, so that measures based on mere journal data are usually additive.
3. 3 Statistics on scientific productivity: Frequency distributions vs. rank statistics
Alfred J. Lotka was the first scientist who tried to find regularity in the publication activity of
authors of scientific publications. In 1926, he published his pioneering study on the frequency
distribution of scientific productivity determined from a decennial index (1907-1916) of
Chemical Abstracts. Lotka concluded “the number (of authors) making n contributions is
about 1/n² of those making one; and the proportion of all contributors, that makes a single
contribution, is about 60 per cent.” Minimum productivity in this model in 1, the number of
authors producing one single paper is denoted by n1, that of authors with maximum
productivity is nmax where nmax > 1 or nmax = 1, according as there is a tie at the first rank or
not.

41
Lotka’s Law is closely linked with another important law formulated by de Solla Price
(1963), namely, that
“half of the scientific papers are contributed by the top square root of the total number of
scientific authors.”
This law is called square root law. Allison et al. (1976) have shown that the square root law
follows from Lotka’s Law only if an additional and not unique assumption is made about the
number of contributions (nmax) by the most active author.
From Lotka’s Law, the following distribution has been derived:
P(X = k) = (6/π2)⋅k–2 , k = 1, 2, 3… ,
that is, no maximum productivity is assumed, or, in other words, the maximum might be
infinite. Unfortunately, Lotka’s Law does not take the possibility of temporary inactivity
{X = 0} into account. Nevertheless, this result can be considered as a rule of thumb even
today, 75 years after its publication.
In 1985, Glänzel and Schubert have proved that a special case of the Waring distribution
satisfies the square root law according to Price without any further condition. Moreover, the
suggested distribution also allows temporary inactivity as the probability of event {X = 0} is
defined. Glänzel and Schubert have called their distribution Price distribution. Being a
special case of the Waring distribution, it can also be derived from the Waring process as
described in Section 2. The probabilities of the Price distributions are as follows
P(X = k) = N·{1/(N+k) – 1/( N+k+1)} , k = 0, 1, 2, 3… ,
Or, if we exclude the event {X = 0}
P(X = k | X > 0) = (N+1)·{1/(N+k) – 1/( N+k+1)} , k = 1, 2, 3… .
Observed Calculated frequency
k frequency Lotka Price*
1 3991 3991.0 3991.0
2 1059 997.8 1063.6
3 493 443.4 492.8
4 287 249.4 284.3
5 184 159.6 185.0
6 131 110.9 130.0
7 85 81.4 96.3
8 64 62.4 74.3
9 65 49.3 59.0
10 41 39.9 48.0
>10 491 705.9 466.8
Figure 3.4 Frequency distribution of scientific productivity according to Lotka
(k = number of papers, Price distribution with N = 0.727)

42
Figure 3.4 presents the original Lotka data as well as the fit on the basis of the Lotka and the
Price distribution according to Glänzel and Schubert, 1985).
One year later, in 1986, Egghe and Rousseau have presented another solution for Price’s
square root law.
Another approach to distributional presentation and analysis of productivity data are rank
frequencies. Figure 3.5 presents the rank frequency table of the distribution of words in
Joyce’s Ulysses according to Zipf (1949). According to Zipf’s Law, the product of rank and
frequency rf should be constant C (in this example C ~ 24,500). Mandelbrot (1963) has
shown that a law of the form f = A{1 + Br}–α is more appropriate. Nowadays, the latter form
is used whenever Zipf’s Law is referred to.
r f r ·f
10 2,653 26,530
20 1,311 26,220
30 926 27,780
40 717 28,680
50 556 27,800
100 265 26,500
200 133 26,600
300 84 25,200
400 62 24,800
500 50 25,000
1,000 26 26,000
2,000 12 24,000
3,000 8 24,000
4,000 6 24,000
5,000 5 25,000
10,000 2 20,000
20,000 1 20,000
29,899 1 29,899
Figure 3.5 The distribution of words in Joyce’s Ulysses illustrating Zipf’s law
(r = rank, f = absolute frequency)
Bradford (1934) discovered his regularity when studying the extent to which literature in a
single discipline is scattered over a range of journals. He found that “if scientific journals are
arranged in order of decreasing productivity on a given subject, they may be divided into a
nucleus of journals more particularly devoted to the subject and several groups or zones
containing the same number of articles as the nucleus when the numbers of periodicals in the
nucleus and the succeeding zones will be as 1: b : b² …”. Let Nn denote the number of
journals in the n-th zone and N0 the number of journals in the core. If the core and each zone
contained the same number of articles then Nn = knN0, where k is the so-called Bradford
coefficient (denoted by b in the above formulation by Bradford). Leimkuhler (1967) has
shown that this law can be reformulated as a particular rank frequency law. Bookstein (1990)
has shown that Leimkuhler’s form is stronger than Bradford’ since Bradford only claimed that
a core can be found obeying his regularity. If we proceed from Leimkuhler’s law, and allow

43
the notion of fractional journals and articles then the Bradford regularity will hold. In the
Leimkuhler version, a distinguished core is, however, not required.
We will just sketch the proof of the equivalence of the two regularities. The basic idea is the
total number of journals N can be obtained by summing up over zones resulting in the
following equation.
N = Σ Ni = Σ0≤i<n kiN0 = N0 (1 + k + k2 + k3 + … + kn–1) = N0(kn – 1)/(1 – k),
Where we assume that we have n zones. Let Y0 denote the number of papers belonging to
each zone (according to Bradford, this number is constant) and Y the total number of papers.
Consequently, we have Y = nY0. Hence we have
Y/Y0 = n = ln {1 + (k – 1)N/N0}/ln k .
Putting b := k–1 yields the form given by Leinkuhler. The reverse of this derivation holds
only if Y/Y0 is an integer.
A B C D
1 93 1 93
1 86 2 179
1 56 3 235
1 48 4 283
1 46 5 329
1 35 6 364
1 28 7 392
1 20 8 412
1 17 9 429
4 16 13 493
1 15 14 508
5 14 19 578
1 12 20 590
2 11 22 612
5 10 27 662
3 9 30 689
8 8 38 753
7 7 45 802
11 6 56 868
12 5 68 928
17 4 85 996
23 3 108 1,065
49 2 157 1,163
169 1 326 1,332
Figure 3.8 Bradford’s data on applied geophysics
(A = number of journals producing the corresponding articles in column B,
B = number of relevant papers found in each journal, C = journal rank
in descending order of productivity and D = cumulative number of papers)

44
If we are not summing up Nn = knN0 over all zones but just over the first r (r ≤ n) zones we
obtain analogously to the above derivation, the following important rank “distribution”:
R(r) = Y0⋅ln {1 + (k – 1)r/N0}/ln k ,
where R(r) is the cumulative number of papers in the first r journals. For r = n, we have, of
course, R(r) = Y. Putting A := Y0/ln k and B := (k – 1)/N0, we obtain the following known form
of Leimkuhler’s law.
R(r) = A⋅ln (1 + B⋅r) , r = 1, 2, 3 … .
Figure 3.6 presents the original data by Bradford’s on applied geophysics.
Rank statistics and ordered samples
An elegant approach to rank statistics is that using Gumpel’s characteristic extreme values
(Gumbel, 1958). Consider a given sample {Xi}i=1,…,n. Assume that the sample is ranked in
descending order, that is,
X
1* ≥ X2* ≥ … ≥ Xn*.
In the “quantile” approach, the statistic Xk* (1 ≤ k ≤ n) is considered the (1 – k/n)-quantile.
Gumbel has defined the characteristic k-th extreme values as
uk = G–1(k/n) = sup{x: G(x) > k/n}; k = 1, 2, …, n,
where n is the sample size, G = 1–F and F is the common cumulative distribution function of
the random variables Xk. Glänzel and Schubert (1988) have shown that there is a sequence of
real values λk ∈ (k–1, k) independent of the distribution of the sample, so that
P(Xk* < uk*) = P(Xk* < G–1(λk/n) ) = 0.5 ,
that is 2λk can be considered the median of a χ2-distribution with 2k degrees of freedom.
Then the modified Gumbel’s characteristic extreme values uk* are the median of the
corresponding ordered statistics Xk*. λk can be approximated by λk ~ (k – 0.3) and we have
limk→∞ (k - λk) = ln 2.
Two types of statistical tests can be derived, particularly,
1. a multi-sample test, for instants, if the extreme values (e.g. the maxima) of sub-
samples are tested for deviation from the corresponding theoretical extreme,
2. a “large-sample” test, if ln n ≥ 101 and deviation can jointly be tested for the first (ln n)
extreme values within the the same sample.
The two tests are described, for instance, in and Glänzel and Schubert (1988) and Schubert
and Telcs (1989). We just mention the following important property. If the distribution of the
random variables of the sample is Paretian, that is, if the common distribution asymptotically
obeys Zipf’s Law (i.e., P(Xk = k) ~ c⋅k-α for α>0 and k >> 1), then the determination of the
modified Gumbel values is not necessary. In particular, we have

45
P(k(ln Xk* – ln Xk-1*) < x) = P(k⋅ln (Xk*/Xk-1*) < x) ~ 1 – e–αx ; k ≤ k0 << n.
Then on the basis of the maximum deviation
Dk0(x) = max | Fk0(x) + e–α
x
– 1| with Fk0(x) = k0–1⋅Σ
χ(k⋅ln (Xk*/Xk-1*) < x),
a simple Kolmogov-Smirnov test can be applied.
Other distribution models for scientific productivity
The application of distribution models to empirical data has shown that the Lotka model could
not properly describe different situations of publication activity. The missing ability to
describe temporary inactivity, decreasing skewness in growing publication periods as well as
different publication habits in the individual science fields may serve just as examples.
Practice has shown that an appropriate distribution model needs at least one or two free
parameters. The Waring distribution described above is one model meeting these
requirements. However, the most versatile model has been introduced by Sichel (1985, 1992).
In this context we mention that both the above-mentioned Waring and negative-binomial
distribution introduced as results of birth processes can be analogously to Sichel’s approach
be derived from Poisson distributions through mixture with continuous distributions. For
instance, we could say that scientific productivity of an author (of a given age and social
status active in a given field) has a Poisson distribution with parameter λ but the parameter λ
itself is random variable as, for instance, age and status of authors may differ. If λ has a
Gamma-distribution than a negative-binomial distribution will be obtain by mixture of the
Poisson with the Gamma distribution. A further mixture with a Pareto-istribution results in a
Waring-distribution.
The generalised inverse Gaussian-Poisson distribution was originally introduced by Sichel as
a comprehensive stationary statistical model for word frequency distribution. Later, he has
applied his model successfully to bibliometrics, too. His basic idea is a two-parameter mixture
(in the generalised case, a three-parameter mixture) of Poisson distributions obtained by
allowing the Poisson parameter λ to have a generalisation of an inverse Gaussian distribution.
The resulting distribution is very complex (and therefore not presented here); the estimation
of parameter is consequently difficult. The goodness of fits exceeds, however, that of all other
models.
3. 4 Factors influencing publication activity, subject characteristics in publication activity
Publication activity is influenced by several factors. Separation of factors could result in
relative simple models like the Poisson model as described in the previous section. At the
micro level, we can distinguish the following four factors.
1. the subject matter
2. the author’s age
3. the author’s social status
4. the observation period

46
At higher level of aggregations (e.g., at institutional or national level), the influence of the
factors age and social status vanishes since populations at this level are rather heterogeneous.
The other two factors (subject matter and publication period) can, however, be taken into
consideration in the sampling process at the meso and macro level, too.
The publication activity in theoretical fields (e.g., mathematics) and in engineering is lower
than in experimental fields or in the life sciences. Experienced authors are expected to be
more productive than “newcomers”. Publication activity in longer observation periods is
obviously greater than in short periods since publication activity is a cumulative process.
An example by Jacobs (2001) illustrates the influence of the status of researchers on their
publication activity (see Figure 3.9). Her sample is based on the activity of a selected group of
academic and research scientists of ten universities of South Africa for a period of five years,
1992-1996.
Figure 3.9 Publication of papers in South African journals
(redrawn from Jacobs, 2001)
Absolute vs. relative publication indicators
When publication patters are analysed in bibliometrics, usually relevant document types are
selected. That is, only those document types that are conveyers of relevant scientific
information are taken into consideration. Such publications are, in particular, journal papers
of the type research articles, letters, notes and reviews. Meeting abstracts, editorial material,
corrections/errata, retractions, book reviews and other document types not listed above are
only objects of special bibliometric studies.
The trend in a unit’s publication output is one of the basic measures in research evaluation.
Practically two approaches are in use, the change of the absolute number of publications in
time and the share of the unit’s publication output in that of a higher aggregation. The second
approach is applied mainly at the meso and macro level. The reason can be found in the
“growth” of the underlying bibliographic databases. Figure 3.10 shows the growth of the SCI
during the period 1980-2000. The underlying edition is the CD-ROM version. The number of
index documents (of the type research articles, letters, notes and reviews) in 1980 was

47
roughly 450,000, the number of journals covered by the database was around 3,250. The
growth of documents is almost perfectly linear with correlation coefficient of r ~ 0.96. The
”pit” in 1984 is caused by changing profile of the database. This is also reflected by the
decrease of journals covered by this edition of the SCI.
Because of the changes in the coverage and the definite growth of the database, the share of
the unit’s publication output in the total or in a unit representing a higher level of aggregation
should be preferred in macro and meso studies.
80%
90%
100%
110%
120%
130%
140%
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Volume year
Growth with respect to 1980
Papers Journals
Figure 3.10 The growth of the SCI database (1980-2000)
In order to visualise in how far database growth can relativise growth of national publication
output, and how dramatic this effect can be, the following example is selected. Figure 3.11
shows the annual change of the Scandinavian share of publications in the world total in two
subject fields in the period 1980-1997. The data have been taken from a recent paper by
Glänzel on Scandinavian science published in 2000. The change of Sweden’s productivity is
most interesting in this context. The Swedish total in the two selected fields, chemistry and
biomedical research has grown from 1980 to 1997 by 74% and 29%, respectively. However,
Sweden’s share in the world total grew only in chemistry but decreased clearly in the field of
biomedical research. Results of this paper and related studies lead to the conclusion that
bibliometric indicators reflect inflationary tendencies that are only partially conditioned by
structural changes and growth of underlying bibliographic databases. Within the framework
of an ongoing project, Persson et al. (2003) have analysed in how far changing patterns of
documented scientific communication caused by intra-scientific factors in the last two
decades are responsible for such inflationary values. According to their study based on SCI
data (CD-Edition), the number papers have grown by 36 percent between 1980 and 1998 that
of the authors has increased by 64 percent. This discrepancy in growth patterns cannot be
explained by the mere growth of documents indexed by the underlying database. The fact that
the growth rate is faster in the case of authors than that of publications forms a contrast to the
observed increasing productivity of authors, too. The average productivity increased in the
period 1980-2000 by 22% where the share of authors with low productivity decreased. These
effects are caused by structural changes in scientific communication, and go much beyond the
policy of database producer in preparing their products. In an earlier study, Kretschmer and

48
Rousseau (2001) have already analysed the breakdown of Lotka’s Law caused by ‘author
inflation’.
Implementations of the above results for research evaluation are two-fold. The most important
consequence of growth of the value of the basic indicators is the need for relative and strictly
normalised indicators in bibliometric trend analyses and medium-term or long-term studies.
Otherwise, these indicators might show a growth where the development is actually
characterised by stagnation or even by decline.
Chemistry
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
S
DK
NO
FIN
Biomedical research
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
S
DK
NO
FIN
Figure 3.11 Annual change of Scandinavian share of publications in the world total
(1980-1997)
3.5 Publication profiles of institutional and national research activity
Besides trends in and shares of publication activity, there is a second important issue in
bibliometric research of scientific productivity at the meso and macro level. This issue is the
analysis of publication profiles. Profile can be determined from different perspectives, for

49
instance, by subject fields (specialisation), by corporate addresses (sectors) and by funding of
research.
3.5.1 Publication profiles by discipline
Two important indicators of specialisation are in use, the share of publications of a given unit
(institution, region or country) in given science areas in the unit’s total publication output and
a relative indicator, the Activity Index or the Relative Specialisation Index, respectively. In the
following, we will define an indicator measuring publication profiles with respect to subject
fields at the national level, but this indicator can readily be redefined for institutional profiles
within a region or country. In particular, it indicates whether a country has a relatively higher
or lower share in world publications in a particular field of science than its overall share in
world total publications. The Relative Specialisation Index (RSI) is closely related to the so-
called Activity Index (AI) long used in bibliometrics (Frame, 1977, Schubert and al., 1989),
which, in turn, is a version of the economists' Comparative Advantage Index. Activity Index
is defined as follows.
AI = the world share of the given country (region) in publications in the given field
the overall world share of the given country (region) in publications
or, equivalently,
AI = the share of the given field in the publications of the given country (region)
the share of the given field in the world total of publications
The Relative Specialisation Index is then defined as
RSI = AI – 1
AI + 1.
It is easy to see that RSI may take its values in the range [-1,1]. RSI = -1 indicates a
completely idle research field, RSI = 1 if no other than the given field is active. RSI < 0
indicates a lower-than-average, RSI > 0 a higher-than-average activity; RSI = 0 reflects a
completely balanced, the “average” situation. It is important to note that RSI reflects a certain
internal balance among the fields in the given unit, that is, positive RSI values must always be
balanced by negative ones: in no unit can all RSI values be positive (or negative).
Four basic paradigmatic patterns in publication profiles can be distinguished:
I. the ‘western model’, that is, the characteristic pattern of the developed Western
countries with clinical medicine and biomedical research as dominating fields,
II. the characteristic pattern of the former socialist countries, present Economies in
Transition and China with excessive activity in chemistry and physics
III. the ‘bio-environmental model’, that is, the pattern most typical for developing and more
‘natural’ countries (e.g., Australia, or South Africa) with biology and earth and space
sciences in the main focus,
IV. the ‘Japanese model’, now also typical for other developed Asian economies with
engineering and chemistry being predominant.

50
Figure 3.12 presents the Relative Specialisation Index of two Scandinavian countries in 1987
and 1997 based on eight major fields of science, particularly, Clinical medicine (MED),
Biomedical research (BRE), Biology (BIO), Chemistry (CHE), Physics (PHY), Mathematics
(MAT), Engineering (ENG) and Earth and space sciences (ESS). Both Scandinavian
countries correspond to Type I, however, Norway’s profile can be considered a mixture of
types I and III changing more and more to type III. Denmark is changing from a country with
almost extremely predominant activity in life sciences to a country representing a more
balanced type I profile (cf. Glänzel, 2000).
Norway
-0.50
-0.25
0.00
0.25
0.50
MED
BRE
BIO
CHE
PHY
MAT
ENG
ESS
1997 1987 World standard
Denmark
-0.50
-0.25
0.00
0.25
0.50
MED
BRE
BIO
CHE
PHY
MAT
ENG
ESS
1997 1987 World standard
Figure 3.12 Relative Specialisation Index of the two Scandinavian countries based on
eight major science fields (1987 and 1997)
Finally we will also given an example for type II. The following figure (Figure 3.13) has been
taken from the 2nd Edition of the European Report on Science and Technology Indicators
(REIST-2, 1997). It presents the relative specialisation profile of Romania and Poland in the
two periods 1984-1989 and 1990-1995. The predominance of natural sciences in these
countries is unusually clear.
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
MED
BRE
BI
O
CHE
PHY
MAT
ENG
ESS
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
MED
BRE
BIO
CHE
PHY
MAT
ENG
ESS
Figure 3.12 Relative Specialisation Index of Romania and Poland
(dotted line: 1984-1989 and solid line: 1990-1995)

51
3.5.2 Publication profiles by sectors
Further distinction can be made, for instance, between academic and industrial research, or,
within the academic sector, between university and non-university research. The analysis of
publication activity in different sectors is a rather delicate question since industry research is
less visible through publications scientific journals than academic research. Moreover, many
publications are of mixed type (e.g., industry/academic or university/non-university academic
research) or the identification of independent or associated institutions proved to be difficult.
The profile of Flemish publications by sectors shown in Figure 3.13 has been taken from the
latest edition of the “Flemish Indicator book” (Debackere, 2003). The underlying publication
period was 1992-2001. Flanders has a typical Western-type profile with predominant research
at universities and other institutions of higher education. The share of public and
governmental research is about one order lower. These data are contrasted by those found for
Hungary in the same period. The share of papers published by authors affiliated with
universities or other institutions of higher education amounts to roughly 60%. By contrast, the
share of public is about 40% that, in turn, is dominated by the Hungarian Academy of
Sciences with nearly one third of all national publications. The share of independent hospitals
with 2% is comparably small. It must be stressed that in both examples the shares cannot be
summed up to 100% since there is an extensive collaboration between sectors, in Hungary,
above all between the Academy of Sciences and the universities.
0.4%
4.9%
6.9%
9.9%
84.7%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90%
I
II
III
IV
V
Figure 3.12 Distribution of Flemish SCI-publications by sectors (1992-2001)
I higher education, II public institution or government, III private institution,
IV hospital (not associated with universities), V others
3.5.3 Publication profiles by funding
Aspects of funding can be uncovered through the analysis of acknowledgement in scientific
publications. Grant Lewison was a pioneer in analysing the use of funding acknowledgement
data as a key factor in determining research 'quality' (e.g., Lewison and Dawson, 1998). He

52
has studied the behaviour of authors in acknowledging their funding (Lewison et al., 1995).
They found that a considerable share of authors do not acknowledge funding. Although main
sources of governmental, public, institutional or industrial funding can be identified, their
extent, however, cannot be estimated reliably on the basis of acknowledgements alone.
3.5.4 Characterising research dynamics of institutions, regions or countries
In order to analyse the research dynamics in selected geopolitical regions, the fields author
and address of the SCI database have been used. Figure 3.13 presents the plot of the indicator
renewal vs. transience in a fixed 5-year publication period according to Glänzel (1992b).
Transients are authors that terminate their publication activity after having published one
single paper (cf. Section 2.4.2). The share of transients in the total scientific community (i.e.,
in all authors) is called Transience Index. By contrast, the Renewal Ratio expresses the ratio
of Newcomers and not-transient Terminators. Figure 3.13 visualises the dynamics of scientific
communities in selected countries.
Figure 3.13 Graphic presentation of the pair of indicators Renewal-Transience
for 30 selected countries in 10 geopolitical regions (according to Glänzel, 1992b)

53
4. INDICATORS OF CITATION IMPACT
4.1 The notion of citations in information science and bibliometrics
In research evaluation, citations became a widely used measure of the impact of scientific
publications. There is controversial discussion about how citations should be interpreted.
Susan Cozzens (1989) has argued that citation is only secondarily a reward system. Primarily,
it is rhetorical-part of persuasively arguing for the knowledge claims of the citing document.
Linda C. Smith, stated that
"citations are signposts left behind after information has been utilized".
Blaise Cronin defined citations as
"frozen footprints in the landscape of scholarly achievement … which bear
witness to the passage of ideas",
but he also referred to certain problems with regard to reference practices as he concluded,
“If authors can be educated as to the informational role of citations and
encouraged to be more restrained and selective in their referencing habits, then
it should be possible to arrive at a greater consistency in referencing practice
generally.”
Problems with citation analysis as a reliable instrument of measurement and evaluation have
been acknowledged throughout the literature. Chapman, for instance, delineated 25
shortcomings, biases, deficiencies, and limitations of citation analysis. Wouters (1997) has
devoted a large monograph on citation culture and in 1998, Leydesdorff has initiated the
discussion about reappraisal of existing theories of citation.
According to Westney (1998), citations are nevertheless indicators of scholarly impact:
“Despite its flaws, citation analysis has demonstrated its reliability and
usefulness as a tool for ranking and evaluating scholars and their publications.
No other methodology permits such precise identification of the individuals who
have influenced thought, theory, and practice in world science and technology.”
In recent studies, Glänzel and Schoepflin (1999) have citations more pragmatically interpreted
as
“one important form of use of scientific information within the framework of
documented science communication,”
however, in general, whether form of nor reason for the concrete information use are not
specified. Although citations cannot describe the totality of the reception process, they give,
according to Glänzel and Schoepflin,
“a formalised account of the information use and can be taken as a strong
indicator of reception at this level.”

54
This statement, though made from the perspective of information science, is completely in
keeping with the above evaluation-related conclusion drawn by Westney.
As mentioned above by Glänzel and Schoepflin, whether form of nor reason for the concrete
information use are taken into account in evaluative studies. However, there are many reasons
for citing publications. Garfield and Weinstock have listed 15 different reasons for giving
citations to others’ work (cf., Weinstock, 1971).
1. Paying homage to pioneers
2. Giving credit for related work (homage to peer)
3. Identifying methodology, equipment, etc.
4. Providing background reading
5. Correcting one's own work
6. Correcting the work of others
7. Criticising previous work
8. Substantiating claims
9. Alerting to forthcoming work
10. Providing leads to poorly disseminated, poorly indexed, or uncited work
11. Authenticating data and classes of facts – physical constants, etc.
12. Identifying original publications in which an idea or concept was discussed
13. Identifying original publications or other work describing an eponymic concept
or term
14. Disclaiming work or ideas of others (negative claim)
15. Disputing priority claims of others (negative homage)
This list is, of course, not exhausting, but some of the above reasons for being cited, for
instance, # 5-7, # 14 and # 15, may illustrate that not all given citations point to quality. But
even criticism expresses the reception of documented scientific information. Heavy criticism
of a certain scientific work can, in a sense, reflect true impact. By provoking constructive
criticism, an erroneous theory may even more contribute to the advancement of a science area
than some sound average study. On the other hand, papers of a controversial nature will
continue to be cited longer.
These examples may just serve as an illustration of the complexity of citation processes. The
general discussion of sociological theories of citations is beyond the scope of this introduction
to citation indicators. For further arguments and a detailed presentation of citation contexts
we, therefore, refer besides the already cited work to the articles by Small (1978, 1982) and
Bonzi and Snyder (1991).
These reasons listed by Garfield and Weinstock can be categorised, on one hand, as ‘positive’,
‘neutral’ and ‘negative’ and, on the other hand, as relevant, less relevant and even irrelevant
or redundant. Figure 4.1 visualises the ‘weight’ of citations.

55
Figure 4.1 The ‘weight’ of citations from the viewpoint of the use of scientific information
The question arises in how far citations express the use of information and the reasons
according to Garfield and Weinstock in reality. Nevertheless, the refereeing system in
documented scientific communication guarantees the observance of relatively strict rules of
providing reference citations.
It might also be worthwhile to list reasons for not giving citations to a colleague’s work, that
is, for not providing reference citations. The first and most important one is lacking relevance
of the topic. Irrelevant topics are obviously not cited. Unawareness is the second reason that
is due to insufficient retrieval of published information relevant for an author’s research work.
Citations omitted by reason of unawareness are sometimes added by referees reviewing
papers prior to acceptance for publication in a journal. According to Garfield (1986) these
papers not recognised by unawareness are whether
“victims of cryptomnesia, an unconscious plagiarism in which creative ideas
expressed as new are actually unrecalled memories of another’s idea, or were
superseded for other reasons remains to be seen.”
Disregard has little do with bibliographic amnesia described by Garfield. Disregard is simply
a reason that is already beyond the borderline to unethical communication behaviour. Results
by colleagues relevant for the author’s research to be published are this way demonstratively
ignored. The fourth reason is a consequence of obsolescence as an expression of ‘natural’
obliteration. Finally, the fifth reason occurs rather seldom in scientific literature, as it is an
expression of the disappearance of the ‘users’ of information. In order words, literature still
being relevant in the context of the research topic is not cited because there are no more
authors who could cite it. We can consider such topics extinct.
As already mentioned in the 2. Section, ageing and obsolescence is expressed by changing
frequency of citations (received or given) over time. So, what is actually measured by
decreasing citation impact? First and above all, decreasing citation impact reflects, of course,
obsolescence. This might be an evolutionary process, that is, cited work gradually vanishes
from reference lists, and is replaced by more recent and more relevant literature. However, it
might be a revolutionary process if a breakthrough has at once made everything obsolete that

56
was so far relevant in this subject. A third form of obliteration occurs if literature is subject to
obliteration by incorporation. This means relevant literature is no longer cited because its
substance has been absorbed by current knowledge; its content has thus become "common
knowledge" (Garfield, 1977, 1986). Garfield (1997) concluded that
"obliteration … is one of the highest compliments the community of scientists
can pay to their author".
The author or inventor has become eponymous. Examples for such eponymic concept
or term in bibliometrics are Bradford’s Law and Lotka distribution.
In this context it should be mentioned that all these arguments and reasons refer to individual
citations. Bibliometrics, however, deals in most cases with citations to larger sets of
publications. As in case of other social processes, a difference in the behaviour of individuals
and the behaviour of large groups or masses can be detected in citation processes, too. Critics
of bibliometric methods argue that citations might be governed by the will and the (sometimes
tendentious) intentions of the authors and may thus result in a deliberate filtering of
information sources (e.g., “citation cliques”). Individual citing may be influenced hereby, but
this phenomenon is certainly not characteristic for the citations to paper sets published by a
larger number of authors. Thus, especially reasons # 10, # 14 and # 15 of Weinstock’s list are
less characteristic in citations to large publication sets. Citation analyses are based largely
upon citation frequency. Several authors in bibliometrics are downright regarding citation
frequencies as a “quality measure”. This interpretation is not only narrowing down the
possibilities of application of citation-based methods, it may also have undesired
consequences at the micro-level, if publications of individuals are studied.
For instance, the fact that a paper is less frequently cited or (still) uncited several years after
publication gives information about its reception by colleagues but does not reveal anything
about its quality or the standing of its author(s). Uncited papers by Nobel Prize winners may
just serve as an example. However,
“if a paper receives 5 or 10 citations a year throughout several years after its
publication, it is very likely that its content will become integrated into the body of
knowledge of the respective subject field; if, on the other hand, no reference is
made at all to the paper during 5 to 10 years after publication, it is likely that the
results involved do not contribute essentially to the contemporary scientific
paradigm system of the subject field in question” (Braun et al., 1985).
4.2 The role of self-citations
Self-citations are a special type of citations: Several forms of self-citations can be
distinguished; two of them are of special importance: Author self-citations and journal
self-citation. Both forms have to be clearly distinguished from each other. Journal self-citation
occurs if a paper published in a given journal is cited by a paper published in the same
journal. A great share of journal self-citations allows the conclusion that the journal in
question is highly specialised, a low share indicates in a sense a “lack of originality”; a low
share of journal self-citations (for instance, < 10%) is, for example, characteristic for review
journals (see, Schubert and Braun, 1993). Journal self-citations are also interesting in the
context of obsolescence studies. Ageing of journal self-citations can significantly differ from

57
that of “foreign” publications. Figure 4.2 (redrawn from Glänzel and Schoepflin, 1995)
illustrates this effect.
Year after publication
Relative frequency
ASR
0123456789
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
all citations self-citations Year after publ ication
Relative frequency
ZWVG
0123456789
0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
all citations self-citations
Year after publication
Relative fequency
LANCET
0 1 2 3 4 5 6 7 8 9
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
all citations self-citations
Figure 4.2 Distribution of citations (black) and (journal) self-citations (grey) over time
(American Sociological Review, Probability Theory and Related fields, The Lancet)
Author self-citation occurs if an author refers to a own paper, that is, if he was the author or
one of the co-authors of the cited paper. The spectrum of these self-citations ranges from the
obvious case, if an author refers to his own work, to more hidden forms, if the co-authors of
the author in question are citing him or themselves in another paper.
Several bibliometricians are inclined to omit at least the obvious types of author self-citations.
In the evaluative context at the micro-level this practice seems to be justified (see Bonzi and
Snyder, 1991, Nederhof et al, 1993). Above all, users in science policy, but sometimes even
the researchers themselves are almost “condemning” author self-citations as possible means
of artificially inflating citation rates and thus of strengthening the authors’ own position in the
scientific community. Other Bibliometricians are rather inclined to regard a reasonable share
of author self-citations as a natural part of scientific communication. According to this view,
it is quite normal that a scientist or a research group refers to the own work. Thus self-
citations do not reveal much about the true impact of research. The share of self-citations in
all citations as well as their share in all references reveals interesting aspects of an author’s or
a research group’s role in the system of science communication. The almost absolute lack of
self-citations over a longer period is just as pathological as an always-overwhelming share.
The first one may indicate lack of originality in research, whilst the latter symptom indicates
isolation and lacking communication. The great number of self-citations – provided, of
course, the share in all citations exceeds not the normal extent – also indicates a successful
and dynamic publication activity since the author or group has then published numerous
papers in refereed journals.

58
MacRoberts and MacRoberts have given a first overview of the unsolved problem of self-
citations in their critical review on problems of citation analysis in 1989.
Beside the discussion on the principles of the role of author-self citations, there is no real
consensus concerning how this type of self-citations should be defined operatively. In
practice, two different approaches to direct self-citations are in use. At the micro level, that is,
on the level of individual authors, a self-citation for an author A occurs whenever A is also
(co-)author of a paper citing a publication by A. This definition cannot, however, be applied to
higher levels of aggregation, that is, when publications and citations are aggregated over sets
of different (co-)authors, and the notion of self-citations is uncoupled from an individual
author A. The definition of self-citations suggested by Snyder and Bonzi (1998) and Aksnes
(2002) can preferably be used at these levels of aggregation. According to this method, a self-
citation occurs whenever the set of co-authors of the citing paper and that of the cited one are
not disjoint, that is, if these sets share at least one author. Although the reliability of this
methodology is affected by homonyms (resulting in Type II errors by erroneous self-citation
counting) and spelling variances/misspellings of author names (resulting in Type I errors by
not recognising self-citation), at high levels of aggregation, that is at the meso and macro
level, there is no feasible alternative to this method.
A recent large-scale analysis of author self-citations by Glänzel et al. (2003) gives interesting
insight into the mechanism of scientific communication.
The first important result of this study characterises to the relationship between self-citations
and foreign citations. Self-citations and foreign citations proved not to be independent
variable. Moreover, the conditional expectation of self-citations for given number of foreign
citation could be characterised by a square-root law. This shows that there is from the
statistical viewpoint nothing arbitrary in self-citations. Thus self-citations are an essential part
of scientific communication. Figure 4.3 visualises this square-root law for author self-
citations.
Figure 4.3 Square-root law for author self-citations
(Plot of expected number of self-citations over number of foreign citations)

59
Analogously to journal self-citations, the weight of self-citations decreases rapidly. The
process is even faster in the case of author self-citations: In the third year after publication, the
distribution of expected self-citations over foreign citations is practically stationary.
Figure 4.4 presents the distribution of author self-citations and foreign citations (i.e., non-self
citations) over time in all fields combined. The figure has been redrawn from Glänzel et al.
(2003).
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Year
Life-time distribution
Self-citation
Foreign Citation
Figure 4.4 Distribution of author self-citations and foreign citations over time
(all fields combined)
The above study has also shown that low visibility goes with high self-citation shares. Figure
4.4 visualises this effect.
y = -0.06x + 0.56
0%
10%
20%
30%
40%
50%
60%
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
MECR
Share of self-citations
Figure 4.4 Plot of self-citations vs. visibility according to Glänzel et al. (2003)
Indicators based on author self-citation proved to be valuable supplementary measures that
can be used both in informetrics and research evaluation. Because of restrictions concerning
their reliability, self-citation indicators should be used in addition to traditional citation
indicators, but not replace them. There is no reason for condemning self-citations in general.
At the level of individual authors or of research teams, the deviation of the share of

60
self-citations from the subject-specific standard might be taken into consideration in
evaluative application of bibliometrics.
4.3 Factors influencing citation impact
The reference items of scientific publications reflect characteristics concerning the “hardness”
of scientific literature. Price (1970) used the share of references not older than five years in all
references of a journal to distinguish between hard science, soft science, technology, and
non-science (Price Index). Moed redefined this index in 1989 as share of most recent
references for individual papers (Price Index per paper). In a large-scale study of 1981, Line
analysed structure of social science literature, and investigated what makes social science
different. Recently, Egghe (1997) and Glänzel and Schoepflin (2001) have published further
studies on these topics.
Another indicator for the distinction between “hard” and “soft” science has been found by
Glänzel and Schoepflin (1999). The percentage of references to serials characterises typical
differences in the communication behaviour in the sciences, social sciences and humanities
(see Figure 4.5).
Perce ntage of r eferences i n serials
Relative frequency (in %)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
SCI SSCI
Figure 4.5 Distribution of the share of references to serials over journals
in the sciences and social sciences
The above question, namely what share of references to serials and non-serials, respectively,
is typical of “hard” and “ soft” sciences can be extended in the following manner. The more
general question arises which forms of information “sources” and “targets” play a role in
science communication. In the social sciences and, even more, in the humanities a
considerable part of cited information is originated in non-science literature. In case of
engineering, the target is in part outside the scientific community; information is used, e.g.,
for the advancement in technology.

61
Authors: Mirza-K Michael-A
Title: Major Depression in Children and Adolescents
Full source: BRITISH JOURNAL OF HOSPITAL MEDICINE 1996, Vol 55, Iss 1-2, pp 57-61
Language: English
Document type: Review
IDS/Book No.: TV978
No. Related Records: 20
No. cited references: 19
Cited references: ANGOLD-A-1995-DEPRESSED-CHILD-ADOL-P127
GOODYER-I-1985-BRIT-J-PSYCHIAT-V147-P517
GOODYER-IM-1993-J-CHILD-PSYCHOL-PSYC-V34-P1409
HARRINGTON-R-1990-ARCH-GEN-PSYCHIAT-V47-P465
HARRINGTON-RD-1993-DEPRESSIVE-DISORDER-P1
JENSEN-PS-1992-J-CHILD-ADOLESC-PSYC-V2-P31
KOVACS-M-1984-ARCH-GEN-PSYCHIAT-V41-P643
KOVACS-M-1986-DEPRESSION-YOUNG-PEO-P435
KOVACS-M-1993-J-AM-ACAD-CHILD-PSY-V32-P8
KOVACS-M-1995-DEPRESSED-CHILD-ADOL-P281
KUTCHER-SP-1989-PSYCHIAT-CLIN-N-AM-V12-P895
KUTCHER-SP-1995-DEPRESSED-CHILD-ADOL-P195
LEFKOWITZ-MM-1978-PSYCHOL-BULL-V85-P716
MANN-T-1929-DISORDER-EARLY-SORRO-P26
PFEFFER-CR-1993-J-AM-ACAD-CHILD-PSY-V32-P106
RIE-HE-1966-J-AM-ACAD-CHILD-PSY-V5-P653
ROCHLIN-G-1959-J-AM-PSYCHOANAL-ASS-V7-P299
STROBER-M-1992-J-CHILD-ADOL-PSYCHOP-V2-P23
WEISSMAN-MM-1987-ARCH-GEN-PSYCHIAT-V44-P747
Figure 4.6 Example for cited information originated in non-science literature
in case of Psychology/Psychiatry
The interpretation of the concept of citation as one important form of use of scientific
information within the framework of documented science communication according to
Glänzel and Schoepflin (1999) does not contradict the application of citation-based indicators
to research evaluation studies, since frequently (or rarely) used information disseminated, say,
by the scientific community of a country or institute is certainly symptomatic for the research
performance of the community in question. Citation based measures are preferably designed
for use in the assessment of research in the natural sciences, the life sciences and
mathematics. They can, however, be applied with certain restrictions to the bibliometrics of
engineering and selected fields of the social sciences.
Citation impact is mainly influenced by the following five factors that are analogously to the
case of publication activity at higher levels of aggregation practically quite inseparable.
1. the subject matter and within the subject, the “level of abstraction”
2. the paper’s age
3. the paper’s “social status” (through the author(s) and the journal)
4. the document type
5. the observation period
Subject Characteristics of Citation Based Indicators
Citation patterns are strongly influenced by subject characteristics. Citation measures are
therefore – without normalisation – not appropriate for cross-field comparisons. Citation
measures for different multidisciplinary papers sets might be distorted by the underlying

62
publication profiles. The following example might illustrate this effect (source year: 1996,
citation window: 1996-1998).
Subject field Mean citation rate
Mechanical, civil and other engineering ..................... 1.12
Mathematics ................................................................ 1.46
Analytical chemistry .................................................... 3.00
Solid state physics ....................................................... 3.06
Neurosciences .............................................................. 4.54
In 1983, Peritz presented a study on the intra-disciplinary differences in citation impact of
theoretical, methodological, and empirical papers in sociology in three prestigious sociology
journals. In natural sciences, theoretical subjects have usually lower impact than applied ones.
The paper’s “social status” and the observation period
The following example (see Figure 4.7) shows the influence of “social status” (through the
journal) and observation period (ranging between one year and 21 years) on citation impact.
The cumulative impact of the prestigious journal of the American Chemical Society
Analytical Chemistry, the German journal Fresenius Journal of Analytical Chemistry
published by Springer-Verlag and the formar Soviet Journal of Analytical Chemistry of the
USSR is compared.
0
5
10
15
20
25
30
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Year
Mean citation impact
J Anal Chem USSR
Anal Chem
Fresenius Z Anal Chem
Figure 4.7 Example the influence of “social status” and observation period
on citation impact
The third example illustrates the influence of a complex of several factors on citation impact.
The impact factor of two journals American Sociological Review (ASR) and The Lancet are
compared in dependence of time. Besides subject peculiarities here the document type is
responsible for the deviating trends of the journals. A considerable part (more than 60%) of
all documents were Letters in 1980.

63
Citation Mean citation rate
window ASR LANCET
1980-80 0.2 0.6
1980-81 1.8 2.4
1980-82 4.3 4.5
1980-85 12.1 9.7
1980-89 20.9 14.0
Figure 4.7 Mean citation rates of two journals in time as a function of time visualising the
influence of several factors on citation impact (publication year: 1980)
4.4 Journal Citation Measures: The Impact Factor
Journal citation measures are one of the most widely used bibliometric tools. They are used in
information retrieval, scientific information, library science and research evaluation. And they
are applied at all levels of aggregation.
The main source of journal citation measures is the annually appearing Journal Citation
Report (JCR). The most important measure is the Impact Factor (Garfield, 1979). The impact
factor for the journal J in the year n is defined as the ratio
IFn(J) = cn
pn-1+pn-2 ,
where cn is the number of citations received in the year n by papers published in the journal J
in the years n–1 and n–2 and the total number of source items (pn-1+pn-2) published in the
journal J in these two years (n–1 and n–2).
The Immediacy Index is defined analogously to the Impact Factor as a journal citation
measure of citations received in the publication year, particularly,
IIn(J) = cn
pn .
The strengths of the Impact Factor lies above all in its independence of the “size” of the
journal, its comprehensibility, stability and seeming reproducibility. On the other hand, some
obvious flaws, but especially the already mentioned uninformed use have provoked critical
and controversial discussions about its correctness and use. In this context, it has also to be
mentioned that ISI’s somewhat poor background documentation concerning the processing of
the data presented in the JCR cannot convince critical users. In particular, the IF and related
journal impact measures can readily be reproduced from the data presented in the Journal
Citation Reports (JCR), however, these very data proved at large not to be reproducible.
Although it is difficult to theoretically define the concept of (journal) impact, there is a wide
spread belief that the ISI Impact Factor is affected or ‘disturbed’ by factors that have nothing
to do with (journal) impact. Consequently, several attempts have been made to improve the
impact factor or to develop additional or alternative journal citation measures. Some of the
main modifications relate to all of the ‘elements’ mentioned in the above-mentioned
mathematical interpretation.

64
- Instead of the mean: other parameters of the distribution (e.g. percentage of uncited
papers or quantiles)
- Instead of integer counting of citations: weighting a citation on the basis of the
journals in which it is made
- Instead of applying a single citing year: application of a range of citing years
- Instead of analysing all (‘citable’) documents: disaggregate articles on the basis of
document type (article + note + review) or content (e.g., theoretical, methodological
and experimental)
- Instead of considering only papers 1-2 years earlier: analysing articles from older
‘ages’
- Instead of synchronic: diachronic, or a combination of the two approaches
Because of its comprehensibility, robustness and its fast availability, the impact factor became
very quickly popular and widely used. The Impact Factor is comprehensible because it
measures the frequency with which an average article published in a given journal has been
cited in a particular year; it is robust because the annual changes of the journals’ Impact
Factors proved to be not dramatic so that in practice one or two years old impact factors are
sometimes used for evaluation purposes where more recent indicators are not available. On
the other hand, time series can be used to monitor the evolution of journals’ citation patterns.
The fast availability of the Impact Factor, finally, is due to the fast indexing, data processing
and the distribution of ISI products. These are in short the most important technical
advantages of the Journal Impact Factor.
On the other hand, according to a number of authors both the Impact Factor and especially the
Immediacy Impact have several serious flaws the consequences of which shall be discussed
here.
1. There is no normalisation for reference practices and traditions in the different fields
and disciplines (Pinski and Narin, 1976).
2. "There is no distinction in regard to the nature and merits of the citing journals"
(Tomer, 1986).
3. There is a bias in favour of journals with large papers, e.g. review journals tend to
have higher impact factors (Pinski and Narin, 1976).
4. Citation frequency is subject to age bias (Asai, 1981, Rousseau, 1988, Glänzel and
Schoepflin, 1995, Moed et al., 1998).
5. There is no indication of the deviations from this statistic (see, for instance, Schubert
and Glänzel, 1983).
6. The average time for a journal article from publication to peak in citations is not
always two years, or as Garfield (1986b) writes "if we change the two-year based
period used to calculate impact, some type of journals are found to have higher
impacts". (cf. also Glänzel and Schoepflin, 1995, Moed et al., 1998)
7. One single measure might not be sufficient to describe citation patterns of scientific
journals.
8. The concept of citable document is not operationalised adequately. As a result,
journal impact factors published in ISI’s Journal Citation Reports are inaccurate for a
number of journals (Moed and van Leeuwen, 1995, 1996).

65
9. In the calculation of JCR impact factors, errors are made due to incorrect
identification of (cited) journals, for instance for the journal Angewandte Chemie –
International Edition (Braun and Glänzel, 1995, van Leeuwen et al, 1997).
The above-mentioned limitations lead very early to the discussion of possible improvements
or alternatives. Among others, Yanovski (1981) criticised certain distortions of the impact
factor and suggested new indicators based on the ratio between citations and references.
Yanovski’s indicator has not found wider use although, for instance, Smart and Elton (1982)
and Todorov (1983) have critically reacted on his approach. Thus, Smart and Elton showed
that the consumption factor and the impact factor are statistically independent which suggests
that these two measures represent distinct journal attributes.
In 1978 Lindsey introduced the Corrected Quality Ratio defined as (number of
citations)3/2/(number of publications)1/2. This formula can be reformulated as the product of
the square root of the impact factor and the number of citations. This approach, however,
lacks interpretability. This might be one reason why this indicator has not found application.
Allison has given an interesting but undeservedly neglected approach in 1980. He used the
statistical function (standard deviation – mean value)/(mean value)2 as an inequality measure
of distributions of scientific productivity and citation impact. The underlying assumption is
that the distribution of authors by the number of publications or by the frequency of citations
is negative binomial. This is the first time that a particular distribution model is assumed for
citation frequency. The indicator is the reciprocal of an estimator of one of the parameters N
of the distribution.
Schubert and Glänzel (1983) have studied the statistical reliability of journal Impact Factors.
In particular, they analysed both the significance of the deviation between the impact factors
of the same journals calculated by different institutes and of the deviation between the impact
factors of two different journals representing the same discipline (see Section 2.2.4). They
have used a similar model as suggested by Allison. The results of this study have strong
methodological and practical influence on journal rankings by impact factors and comparative
analyses in research evaluation.
According to Asai (1981) the period count based on a month produces more accurate statistics
than that based on a year. The author introduces an Adjusted Impact Factor which counts the
weighted sum of citations over a period of four years instead of one year as in case of the
original Impact Factor.
The most sophisticated improvement has been presented by Narin and Pinski. Whereas in
calculating the impact factor and the immediacy index all citations are equally weighted, the
"influence methodology" suggested by Pinski and Narin (1976) provides for each journal a
size-indepedent Influence Weight determined by the number of the journal’s citations and
references. The calculation is based on an iteration procedure involving great expense.
Weighting citations by these influence weights, the influence per publications and the total
influence can be calculated. Geller (1978) suggests a 'corrected' influence weight that could be
interpreted as the probability that a given journal will be cited from the other journals.
Because of the troublesome calculations and the lack of expressive interpretability of the
results, the method has gained few adherents.

66
In the last two decades, several bibliometric research centres therefore succeeded in
calculating their own journal impact measures on the basis of the bibliographic databases of
the ISI. Since 1995 citations are often counted in a three-year or four-year observation period:
in the year of publication and the two subsequent years at the ISSRU in Hungary and at
RASCI in Germany. This three-year citation window proved to be a good compromise
between the relatively fast obsolescence of technology oriented literature, of most areas in life
sciences, of experimental physics literature, on one hand, and of the slowly ageing theoretical
and mathematical topics in physics, on the other (see, Glänzel and Schoepflin, 1995 and Moed
et al., 1998). CWTS has also used four-year observation period in several studies. An
overview of applications, problems and limitations of the Impact Factor has been given by
Glänzel and Moed (2002).
4.5. Towards relative citation indicators
The Citation Rate per Publication (Mean Observed Citation Rate) is a fundamental citation
based measure that can be applied to all levels of aggregation. MOCR is called Citations per
Publications (CPP) at CWTS. The impact factor discussed in the previous section is a special
case of a mean observed citation rate.
Peter Vinkler is using mean citation rates in combination with journal impact factors for
institutional evaluation of research performance (micro and meso level). He has defined
several indicators on the basis of journal impact, field impact and observed citation rates. By
averaging weighted indicators and constructing relative indices, Vinkler created complex
measures designed for application to the evaluation of research performance of individuals
and departments (for instance, Vinkler, 2002).
The Expected Citation Rate per Publication (Mean Expected Citation Rate). The expected
citation rate of a single paper is defined as the average citation rate of all papers published in
the same journal in the same year.
Note that these journal averages are not necessarily identical with the Journal Impact Factors,
as they are defined and listed in the Journal Citation Report volumes of the SCI (Garfield,
1975). Any appropriate citation window can be used instead of one year citation window to
publications of the two preceding years as used in the Journal Citation Report (JCR).
For a set of papers assigned to a given unit (e.g., institution, country or region) in a given field
(subfield) the indicator is the average of the individual expected citation rates over the whole
set. At CWTS this indicator is called Mean Citation Rate of Journal Packet (JCSm).
The mean citation rate of a subfield can be considered a second expectation of a paper
published in this discipline. At CWTS, this measure is denoted by FCSm.
In order to overcome the shortcomings caused by subject characteristics, and to find a fair
basis for comparisons, citation measures can be normalised by a proper reference standard.
The impact factor of the journal in which the papers have been published and/or the subfield
to which they can be assigned may serve as such reference standard. Relative citation
indicators are measures which gauge observed citation impact against the expectation or
against a proper reference standard.
- The Relative Citation Rate (RCR) is defined as the ratio of the Citation Rate per
Publication to the Expected Citation Rate per Publication, that is,

67
RCR = MOCR/MECR (see, for instance, Schubert and al., 1989). A version of this
measure, particularly, CPP/JCSm is used at CWTS.
Both MOCR and MECR have to be determined for exactly the same publication year and
the same citation window!
RCR measures whether the publications of a unit attract more or less citations than
expected on the basis of the average citation rates of the journals in which they appeared.
Since the citation rates of the papers are gauged against the standards set by the specific
journals, it is largely insensitive to the big differences between the citation practices of the
different science fields and subfields. Therefore, this indicator is uniquely suitable for
cross-field comparisons.
− The Relative Citation Impact Index (RCII) is closely related to the RCR. Similarly to the
way RSI was derived from AI, RCR can be normalised into the range [-1,1] by the
transformation
RCII = RCR – 1
RCR + 1.
RCII = -1 corresponds to uncitedness, RCII = 1 to the fictitious case of infinite number of
citations; RCII < 0 means lower-then-average, RCII > 0 higher-than-average citation rate,
RCII = 0 if the set of papers in question attracts just the number of citations expected on the
basis of the average citation rate of the publishing journals.
- The Normalised Mean Citation Rate (NMCR) is defined as the ratio of the Citation
Rate per Publication to the weighted average of the mean citation rates of subfields.
A similar measure (CPP/FCSm) is used at CWTS.
TR
U
A
RURO
BG
PL
HU
S
K
CZ
NO
IS
CH
U
K
S
E
P
NL I
IRL
EL
F
FIN
D
D
K
B
A
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0. 5 1.0 1.5 2.0 2.5
MEC
R
MOCR
High ci tati on rate i n low impact journal
s
High ci tati on rate i n high impact journal
s
Low cit ation r ate in l ow impact j ournal
s
Low cit ation rate i n high impact journal
s
Figure 4.8 Comparison of citation impact of 26 European countries in mathematics
(source year: 1993, citation window: 1993-1995)

68
The two relative indicators can large deviate from each other. The reason for that lies in the
publication strategy of the units of analysis. If, for instance, RCR is significantly higher
(lower) than NMCR then authors assigned to the unit in question publish in lower(higher)-
than-average journals (with respect to the field).
Figure 4.9 Comparison of the normalised citation impact of departments of the medical
faculty of the University Antwerp (1992-1998) using a simple statistical test
according to van Leeuwen et al. (2001)*
* Each circle or square represents one department; black coloured squares above (below) the horizontal
reference line represent departments for which the impact (CPP) is significantlyabove (below) the world
average (FCSm).

69
Observed citation based indicators and their expectations can be presented in relational
charts. Figure 4.8 presents the plot MOCR vs. MECR in mathematics. The indicator values
are based on publication data of the 1993 volume of the SCI and the 3-year citation window
19993-1995. According to the definition, MOCR and MECR for subject areas defined on
journal basis coincide. The MOCR for mathematics in 1993 amounts to 1.23. Since the
selected countries are rather large, the “random error” of MOCR being proportional to n½,
where n is the sample size, is relatively small (cf. Section 2.4.4). However in countries with
less than 100 publications, the standard deviation of MOCR is already measurable. The
standard deviation of MECR is practically zero since the samples are here based on the
underlying journals, that is, is roughly corresponds to that of the total field.
Standard deviation of mean citation impact at the meso level (for instance that of research
groups or departments) is usually significantly greater than that at the macro level. Increasing
the “random error” by one order has dramatic consequences on conclusions drawn from
comparative analyses. The plot in Figure 4.8 shows that a quite large deviation of the mean
citation rate of a research group or department from its expectation (or from another one) does
not necessarily be considered significant.
Share of uncited or cited papers
Although bibliometric indicators applied at a national or supra-national level are decidedly
more reliable than their meso and micro level pendants, their use does not lack some typical
problems, either. In particular, the higher the level of aggregation the greater the
heterogeneity of the population and the statistical distributions underlying the indicators get
extremely polarized. Thus, the complexity of the national/supranational citation patterns can
scarcely be reflected by a single indicator such as the average citation rate. In other words,
one single parameter is not sufficient for describing citation patterns otherwise the expected
value would uniquely determine the shape of the distribution. Figure 4.10 might just serve as
a counterexample. The two selected journals Trends in Genetics and American Journal of
Respiratory and Critical Care Medicine have almost the same mean citation rate, namely 7.0
and 6.9, respectively (publication period 1995-1996, 3-year citation windows). The shapes of
the two distributions is, however, characterised by different features. The share of uncited or
cited papers being the estimate of the corresponding probabilities P(X = 0) and
P(X ≥ 0) = 1 - P(X = 0), respectively, could, of course, serve as an obvious addition measure.
Moed et al. (1999), however, showed that the two indicators are practically not independent.
The standard error of shares such as the share of cited papers (fc) can be calculated similarly
to the formula given in Section 2.4.4 for the impact. In particular, we have
D(fc) = pc (1–pc)/n , where pc is the corresponding probability of being cited. The standard
error of the share of uncited papers coincides with that of the previous one since p0 = 1 - pc.

70
0%
5%
10%
15%
20%
25%
0 2 4 6 8 1012141618202224
Citations
Relative frequency
Figure 4.10 Citation distributions of two journals with same impact and different shape
(Trends in Genetics (solid line) and American Journal of Respiratory and
Critical Care Medicine (dotted line))
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0123456789101112131415
x
N
JAMA
PHYSICA B
J AM PATH
J NAT PROD
Figure 4.11 Plot of estimated N values vs. mean x for 3370 journals published in 1995-1996
and cited in 3-year citation windows

71
The approach by Allison (1980) defines a second parameter that is practically independent of
the mean. According to section 4.4, this is the reciprocal of the parameter N in the negative-
binomial model by Glänzel and Schubert (1995). Figure 4.11 presents the plot of estimated
parameter N vs. mean x for all journals published in 1995-1996 and cited in 3-year citation
windows, each. Except for extremely low impact, there is no significant correlation. Four
journals have bee selected to represent the four quadrants (low impact with small and large
parameter N; high impact with small and large parameter N).
Highly cited publication characetrising the ‘high end’ of citation impact
In the last subsection, we have seen that uncited papers may give further information on the
degree of polarisation, concerning the ‘low end’ of the distribution. From the viewpoint of
evaluative analyses, characteristics of the ‘high end’ of the distribution are by far more
relevant. Data on highly cited papers and authors have regularly been presented (for instance
by Garfield), although a consensus on the exact definition and meaning of the term highly
cited does not exist as yet.
To determine the authors or papers with most citations usually a fixed number (Vlachý, 1986)
of items or a certain quantile is selected from a rank statistic (for instance, ‘the top decile
papers’ (Hofer Gee and Narin, 1986)). In some lists, papers or authors are considered highly
cited if the number of citations received by them simply exceeds a given fixed value (for
instance, “papers cited more than 400 times” (Garfield)). These a priori criteria reflect
neither field-specific peculiarities nor deviations caused by the particular choice of
publication and citation periods. At best empirical results may help to find an individual
number of items or an individual quantile for each subject field and time period (for example,
according to Garfield: “in some fields with fewer researchers, 100 citations may qualify a
work”). According to Glänzel and Schubert (1992) thresholds determining highly cited papers
should meet the following criteria:
1. They should be great enough to guarantee that the selected items form a real elite.
On the other hand, it should be small enough to obtain a statistical population of
elite items.
2. They should be flexible in order to compensate for the unequal publication and
citation behaviour in different science fields and to allow "fine tuning" in order
to adjust the size of selected groups.
3. The threshold should be time invariant with respect to the citation window.
Thresholds for highly cited papers could be defined as follows. We say that a paper highly
cited if the number of citations it has received during a given period exceeds
ks(j) = s·max(1,xj), where xj is the average citation rate of the reference standard. The mean
citation rate of journal in which the paper has been published or of the subject to which the
paper belongs or a combination of the two might be used as the reference standard. The same
citation window has to be used for both the citation rate of t he paper and the chosen reference
standard.
In verbal terms, a paper is considered highly cited if it has received at least s citations, and the
number of citations amounts at least s-times the reference standard. The coefficient s is
responsible for adjusting the final group size of selected papers. The term max(1,xj) contains
a fixed component which has two functions, it filters noise and makes sure that the mean
citation rate of highly cited papers increases with rising thresholds, i.e., with growing s.
Despite the advantages of this approach, there is still something arbitrary in the definition of

72
the coefficient s. Moreover, it might occur that a highly cited paper (meeting to the above
criteria) does not classify for the selection if a larger citation window is chosen and the
threshold has to be redefined for e new reference standard. This makes the “theory” of high
citations from the dynamic perspective somewhat instable. However, this applies to almost all
solutions discussed here.

73
5. INDICATORS OF SCIENTIFIC COLLABORATION
Scientific collaboration has become one of the favourite topics in bibliometric research.
Collaboration pattern can be studied at almost all levels; co-operation of individual scientists
has, for instance, been investigated in the context of social stratification in science (e.g.,
Kretschmer, 1992a,b). The published results of intra- and extramural collaboration have been
compared at the institutional level, and the strongly intensifying domestic and international
collaboration has served as a base of several bibliometric macro studies.
5.1 Co-authorship as a measure of scientific collaboration
Bibliomterics is measuring scientific collaboration by means of co-publication statistics. Of
course, the question arises in how far collaboration is reflected by corresponding
co-authorship. In a recent study, Laudel (2002) has shown on the basis of a sample of
interviewed scientists that a major part of collaboration is not acknowledged either through a
proper acknowledgement or through co-authorship. However, this rather applies to so-called
intramural collaboration, that is, to collaboration within a department, research group or
institute. Extramural collaboration, above all international collaboration, is, however, well
acknowledged. Results of collaborative research at this level are reflected by corresponding
co-authorship of the published results that can, in turn, be analysed with the help of
bibliometric methods.
Besides the economic and political factors, many intra-scientific factors (see, for example,
studies by deB. Beaver and Rosen 1978, 1979, Luukkonen et al., 1992, 1993), especially
changing communication patterns and increasing mobility of scientists, are also influencing
collaboration. These factors motivates co-operation in "less expensive" areas such as pure
mathematics and theoretical research in social sciences, too. Analogously to the
Garfield/Weinstock list of reasons for providing citations, there is also a compilation of
motivation for collaborative research. DeB. Beaver (2001) lists the following 18 purposes for
which people collaborate:
1. Access to expertise.
2. Access to equipment, resources, or “stuff” one doesn’t have.
3. Improve access to funds.
4. To obtain prestige or visibility; for professional advancement.
5. Efficiency: multiplies hands and minds; easier to learn the tacit knowledge that
goes with a technique.
6. To make progress more rapidly.
7. To tackle “bigger” problems [more important, more comprehensive, more difficult,
global].
8. To enhance productivity.
9. To get to know people, to create a network, like an “invisible college”.
10. To retool, learn new skills or techniques, usually to break into a new field, subfield,
or problem.
11. To satisfy curiosity, intellectual interest.
12. To share the excitement of an area with other people.

74
13. To find flaws more efficiently, reduce errors and mistakes
14. To keep one more focussed on research, because others are counting on one to do
so.
15. To reduce isolation, and to recharge one’s energy and excitement.
16. To educate [a student, graduate student, or, oneself]
17. To advance knowledge and learning.
18. For fun, amusement, and pleasure.
Kretschmer (e.g., 1994) has analysed aspects of social stratification in scientific collaboration
at the micro (individual) level. Main findings are that extramural collaboration is
characterised by similarity of the social status whereas intramural collaboration shows
significant differences of the social status of the co-authors.
Scientific collaboration – as measured by means of co-authorship patterns – has considerably
increased during the last decades at all levels of aggregation. In the 90s the rapid increase has,
however, somewhat slowed down.
The most frequently used aggregation levels in the context of co-publication studies are the
level of individual authors, extramural domestic, collaboration between sectors (e.g.,
university/higher education, non-university academic, industry) and international
collaboration.
The following example shows the increase at the level of individual authors. Figures 5.1a and
5.1b present the distribution of co-authors over publications in 1980, 1986, 1992 and 1996 in
two science areas, namely in Biomedical research and in Mathematics (cf., Glänzel, 2002).
Figure 5.1b shows that in 1996 already more that 60% of all mathematical papers was multi-
authored.
0%
5%
10%
15%
20%
25%
30%
35%
40%
12345>5
Number of co -authors
Relative frequency
1980 1986 1992 1998
Figures 5.1a The distribution of co-authors over papers in ‘Biomedical research’

75
0%
10%
20%
30%
40%
50%
60%
70%
12345>5
Number of co -authors
Relative frequency
1980 1986 1992 1998
Figures 5.1b The distribution of co-authors over papers in ‘Mathematics’
Although the increase of collaboration itself is already a remarkable phenomenon, the
question arises in how far increasing collaboration interacts with other processes. The
assumption that collaboration might increase publication output is almost obvious. If an
author is part of a stable team and as such co-author of its publications, he/she shares all
papers with the other members of the team and this will be accordingly reflected by integer
publication counts. Although this idea suggests itself, it could not be proved empirically. The
following example taken from the above by study by Glänzel (2002) contradicts any
common-place notion. Figure 5.2 presents the plot of average productivity vs. average
co-operativity in three selected fields in 1996.
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
123456789>9
Mean co-operativity
Mean publication activity
Mathematics Chemistry Biomedical research
Figure 5.2 Plot of average productivity vs. average co-operativity in three selected fields
in 1996 according to Glänzel (2002)
For authors in all three fields there is a peak of productivity close to the average
co-operativity value characteristic for the field in question. For instance, in biomedical
research the maximum productivity is reached for teams with 6 co-authors, whereas in
mathematics, mean publication activity takes its maximum value in case of 1-2 co-authors.
Otherwise, no unambiguous “effect” on publication activity can be found for the number of

76
authors involved. Collaboration is thus not associated with higher productivity at the
individual authors. In mathematics, productivity is even slightly decreasing with growing
co-publication activity. Although “team work” exhibits higher productivity than single
authorship in the two other fields, beyond a field-characteristic level productivity distinctly
decreases with growing co-operativity. Braun et al. (2001) have shown a similar effect in the
field of neuroscience.
The positive effect of collaboration and especially of international collaboration on citation
impact has been shown in many studies, although international collaboration does not always
pay for all partners involved (cf. Glänzel, 2001). Figure 5.3 visualises this effect by presenting
the plot of mean citation rate vs. number of co-authors for domestic and international
collaboration for papers published in 1980 and 1998 in all fields combined. For this example,
a 3-year citation window has been used.
y = 0.492x + 1.501
R2 = 0.912
y = 0.506x + 2.798
R2 = 0.772
y = 0.661x + 0.916
R2 = 0.947
y = 0.927x + 0.469
R2 = 0.964
0
2
4
6
8
10
12
14
123456789101112
Number of co-authors
Mean number of citations
1980 D 1980 I 1998 D 1998 I
Linear (1980 D) Linear (1980 I) Linear (1998 D) Linear (1998 I)
Figure 5.3 Relationship between number of co-authors and mean citation rate
controlling for international collaboration (all fields combined)
5.2 Indicators of co-operativity and co-publication networks
Most important measures of co-operativity are, for instance, the number and share of
co-authored papers of a unit, of joint publications of different units, of the strength of
co-authorship links and the profile and citation impact of co-publications. The first
comprehensive study on international collaboration using co-operativity measures has been
published by Schubert and Braun in 1990.
Figure 5.4 shows the dramatic increase of international collaboration on the basis of SCI
publications. Nevertheless, it should be mentioned that this overall trend does not apply to all
countries; the share of internationally co-authored publication, for instance, in Turkey, Korea
and Saudi Arabia decreased. Some changes are obviously consequences of changes of
political and/or economic systems in the countries or regions in question. Examples are the
Economies in Transition in Eastern Europe and South Africa.

77
Rank Country 1995/96 1985/86
Papers Share Papers Share
1 Thailand 1131 64.2% 583 46.5%
2 Hungary 5213 50.3% 4670 26.5%
3 Portugal 2870 50.1% 813 37.8%
4 Czech Republic 5587 49.1% n. a. [18.9%]1
5 Switzerland 20872 47.5% 13506 32.1%
6 Poland 12374 45.7% 9261 20.2%
7 Chile 2496 45.4% 1557 25.5%
8 Belgium 14695 45.0% 9009 28.1%
9 Venezuela 1137 44.9% 733 30.8%
10 Romania 2069 44.7% 1301 15.0%
11 Slovenia 1264 44.6% n. a. n. a.
12 Slovakia 2815 44.3% n. a. [18.9%]1
13 Denmark 11809 43.3% 8387 24.2%
14 Croatia 1401 43.0% n. a. n. a.
15 Mexico 4960 42.6% 1997 29.9%
16 Austria 9479 42.6% 5439 23.8%
17 Brazil 9417 41.7% 3918 26.9%
18 Bulgaria 2503 40.4% 2611 20.9%
19 Ireland 3162 40.3% 1807 25.0%
20 Norway 7131 40.0% 5129 23.4%
21 Sweden 23698 39.0% 17143 21.9%
22 Greece 5556 37.5% 2629 25.4%
23 Hong Kong 4191 37.5% 1179 23.0%
24 Israel 14067 37.1% 11142 25.0%
25 Finland 10361 35.6% 6143 19.3%
26 Netherlands 29773 35.4% 18153 19.8%
27 France 73925 34.2% 47640 20.3%
28 Belarus 1653 33.6% n. a. n. a.
29 Germany 93683 33.3% [58164]3 [19.4%]3
30 Italy 46757 33.1% 23913 21.1%
31 Argentina 5167 32.0% 3108 13.2%
32 Ukraine 6691 31.3% n. a. n. a.
33 New Zealand 5967 31.3% 4729 15.8%
34 Egypt 3266 31.0% 2409 21.9%
35 Yugoslavia 1326 30.8% 2387 30.1%
36 Canada 54369 30.6% 43001 18.6%
37 Spain 29538 30.0% 10409 15.1%
38 PR China 18861 28.8% 6442 23.2%
39 Singapore 2676 28.8% 760 23.7%
40 UK 110898 27.2% 86721 14.4%
41 South Africa 5448 27.0% 5893 11.8%
42 South Korea 10007 26.8% 1221 27.3%
43 Australia 30139 26.4% 21200 14.5%
44 Russia 44664 25.5% n. a. [3.3%]2
45 Saudi Arabia 1797 23.7% 1173 26.5%
46 Turkey 4798 21.4% 926 25.9%
47 USA 403056 18.1% 340275 9.5%
48 Taiwan 11594 17.5% 1883 23.5%
49 India 21449 15.2% 21335 8.5%
50 Japan 108019 14.4% 67234 7.3%
1 Czechoslovakia 2 Soviet Union 3 without GDR
Figure 5.4 Change of national publication output and share of international co-publications
(all fields combined, 1985/86 vs. 1995/96)
Frequently used measures for the strength of links are Salton’s measure and the Jaccard
Index. In addition, the extent of multi-nationality of collaboration can be studied. The

78
mathematical-methodological background of these measures will be introduced in the
following section. Nevertheless, two examples for the use of Salton’s measure in the context
of international co-publication structures will be given at this place. Figures 5.5 and 5.6
visualise networks of international co-publications on the basis of the strength of
collaboration links between country pairs. Multinational links have been split into the
corresponding set of bilateral links. One has, consequently, to distinguish between the number
of co-publications and of co-authorship links.
FIN
SU
NL
IL
NO
PL
D
B
S
F
DK
BR
UK
USA
CAN
A
CH
I
E
H
CS
IND
EL
JP
PRC
TW
AUS
NZ
KOR
ZAF
AR
CL
EG
SA
HK
IRE
P
MX
BG
RO
TH
SG
TR
VE
YU
DDR
Figure 5.5 Co-authorship map for 50 most active countries in all fields combined in 1985/86
based on Salton’s measure (dotted line
≥
1.5%, solid line
≥
2.5%)
FIN
RUS
NL
IL
NO
PL
D
B
S
F
DK
BR
UK
USA
CAN
A
CH
I
E
H
CZ
UA
IND
EL
JP
PRC
TW
AUS
NZ
KOR
ZAF
AR
CL
SL
EG
SA
SK
HK
IRE
P
CR
MX
BG
RO
TH
SG
TR
VE
YU
BY
Figure 5.6 Co-authorship map for 50 most active countries in all fields combined in 1995/96
based on Salton’s measure (solid line
≥
2.5%, thick line
≥
5%)

79
The two Figures 5.5 and 5.6 redrawn from Glänzel (2001) show that the share of international
papers has grown in most countries; it also substantiates that international collaboration has
intensified and the density of the network has increased. Moreover, the structure itself has
changed. Although the two examples are almost self-explaining, some comments might help
their interpretation.
- International scientific collaboration in the first period was not as intense as ten years
later, therefore, lower thresholds (rij) of Salton’s measure had to be used in Figure 5.5.
As the lower threshold for medium (very) strong links, rij = 1.5% (2.5%) has been
chosen. Values of Salton’s measure exceeding 5% did not occur in 1985/86. The
position of the countries on the map is intended to reflect the ‘natural geographic
order’ as much as possible, and to express, at the same time, the structure defined by
the co-authorship links. Six clusters of unequal size, namely, a big one including
Western Europe, USA and Canada and two smaller ones with the Scandinavian and
the Eastern European countries, respectively, can be found. There are further clusters,
one including Australia and New Zealand, one consisting of Egypt and Saudi Arabia
and a sixth one with Brazil and Argentina.
- The co-publication map presented in Figure 5.6 shows a quite different situation ten
years later. Since the intensity of links has increased considerably from the 80s to the
90s, the corresponding thresholds had to be modified. The dense network of links had
otherwise made the map unintelligible. Links with strength below 2.5% have,
therefore, not been plotted. In addition, co-publication links stronger than 5% are
represented by thick lines (see Figure 5.6). The changes are striking. First, the overall
strength of links has increased; thus dotted lines in Figure 5.5 are regularly replaced by
solid ones in Figure 5.6. Second, the network of co-publication links became denser
although the lower threshold of 1.5% has been omitted in 1995/96. Third, a structural
change can be observed. The Arabian cluster is still isolated, and has not changed. The
South American cluster has undergone some structural changes. A tiny new cluster
formed by the P.R. China and Hong Kong arose in Far East. The link between these
two countries (5.9%) is one of the strongest in the period under study (a couple of
years before the crown colony returned to China). The biggest cluster includes Europe,
the USA and Canada. A strongly cross-linked EU cluster connected to the USA, a
coherent Scandinavian cluster connected through Denmark and Sweden with the rest
of the North American/European main cluster and a loosely connected
Central/Eastern-European cluster joined to the main cluster through Germany and – as
a new development – Poland playing jointly with Russia the role of a newly-fledged
node in Eastern Europe.
Co-authorship is a symmetric (bi- or multidirectional) phenomenon; therefore, most
bibliometric measures of international collaboration derived from co-publication analysis are
symmetric. The maps presented in Figures 5.5 and 5.6 reflect mutual links but do not reveal
anything about specific unidirectional ‘affinities‘ of a country for co-authorship with other
countries. However, it is possible to create ‘asymmetric’ measures of ‘co-authorship affinity’
to characterise the relative ‘importance’ of other countries for countries under study. With the
help of the shares of joint papers with other countries in all co-publications and their share in
the world total, a certain asymmetry can be uncovered in case of mutual affinity. Figure 5.7
presents the bi-literal codes of the 10 most important partner countries of Germany, France,
USA and Japan (column A), the number of joint papers in all fields combined (column B), the
percentage share of joint papers in the internationally co-authored papers of the selected

80
country (column C) together with the percentage share of the total number of publications of
the same set of countries in the world total minus the number of publications of the selected
country, Germany, France, USA and Japan, respectively (column D). The latter two values
are identical if a country is exactly as important for the country under study as it is for the rest
of the world. The values in column D may, in a way, serve as expectation for the C values.
The deviation from this ideally balanced situation is in reality often considerable. There is, for
instance, a clear asymmetry in the collaboration link Germany–Japan, since Germany is more
important for Japan as expected, but Japan’s importance for Germany is significantly below
expectation. The same applies to the link USA–Japan. There is also a slight asymmetry in the
link between USA and Germany, whereas the link between Germany and France can be
characterised as a well-balanced mutual relationship. The examples presented in Figure 5.7
are taken from the study by Glänzel (2001) on national characteristics in international
scientific co-authorship relations.
Germany France USA Japan
A B C D A B C D A B C D A B C D
US 9381 30.03% 37.72% US 6701 26.47% 37.04% DE 9381 12.84% 12.34% US 7268 46.67% 38.23%
UK 3780 12.10% 10.38% DE 3528 13.94% 8.61% UK 9296 12.73% 14.61% DE 1499 9.63% 8.89%
FR 3528 11.29% 8.77% UK 3295 13.02% 10.19% CA 8703 11.91% 7.16% UK 1479 9.50% 10.52%
RU 2626 8.41% 4.18% IT 2547 10.06% 4.30% JP 7268 9.95% 14.23% CA 999 6.41% 5.16%
CH 2567 8.22% 1.95% CH 1820 7.19% 1.92% FR 6701 9.17% 9.74% FR 885 5.68% 7.01%
IT 2242 7.18% 4.38% ES 1785 7.05% 2.71% IT 5112 7.00% 6.16% CN 841 5.40% 1.79%
NL 1946 6.23% 2.79% BE 1635 6.46% 1.35% CH 3145 4.31% 2.75% KR 619 3.97% 0.95%
JP 1499 4.80% 10.11% CA 1593 6.29% 5.00% NL 3121 4.27% 3.92% IT 606 3.89% 4.44%
AT 1468 4.70% 0.89% RU 1445 5.71% 4.10% IL 2976 4.07% 1.85% RU 581 3.73% 4.24%
SE 1259 4.03% 2.22% NL 1326 5.24% 2.74% AU 2859 3.91% 3.97% AU 518 3.33% 2.86%
Figure 5.7 Co-authorship affinity for four selected countries ranked by share of joint papers
(A = Country, B = number of joint papers, C = Share of joint papers in all international papers,
D = Share of partner country in the world total minus country under study)
Figure 5.8, finally, gives an outline of a possible organisation and the sketch of a
methodological scheme of a complex analysis of international co-publication patterns
according to the above-mentioned study by Glänzel (2001).
1.1.2.
Research profiles
of domestic and
international papers
1.1.1.
Share of international
co-publications
1.2.2.
Analysis of
(unidirectional)
co-authorship affinity
1.2.1
Mapping mutual
co-authorship links
1. Publication activity
2.1.1.
"Publication strategy"
of domestic vs.
international papers
2.2.3.
Citation analysis of
co-authorship links
by country pairs
2.2.2
Citation distributions
over domestic and
international papers
2.2.1.
Citation impact of
domestic vs. inter-
national papers
2. Citation impact
International Co-authorship Patterns
Figure 5.8 Sketch of a possible methodological scheme of the analysis
of international co-publication patterns

81
6. INDICATORS AND ADVANCED DATA-ANALYTICAL
METHODS
The previous section has already shown that bibliometric analyses might go far beyond direct
comparison of indicator values and ‘linear ranking’. The example of co-publication networks
and unidirectional collaboration links, as well as the distributional approach to ‘scientific
productivity’ and citation impact have shown that two- and multi-dimensional presentation
might become necessary to describe underlying phenomena in an appropriate way. This
requires advanced data-analytical techniques. Since statistical standard methods as provided
by statistical programme packages can often be used (for instance, cluster analysis and
multidimensional scaling), we will restrict this section to the underlying bibliometric
rudiments yielding measures that might serve as input of statistical standard techniques.
Statistical groundwork of such analyses is multivariate data-analysis techniques, that is,
methods allowing the simultaneous analysis of quantitative relations between several
variables. The aim of these analyses is, in particular, grouping (clustering) of bibliometric
elements or units on the basis of similarity properties and/or measuring the ‘distance’ between
them. Most bibliometric measures serving as a basis of these data-analytical methods can be
derived from bibliometric transaction matrices. The visualisation of the results is called
bibliometric mapping. Dynamic maps are used to monitor the change of structures in time.
6.1 Bibliometric transaction matrices
Transaction matrices are square matrices of statistics giving transactions between bibliometric
elements (e.g. papers or patents) and units (such as journals, countries etc.). These matrices
have first been analysed by Price in 1981.
Joint references and citations, co-authorship, citation processes, attendance at conferences can
be considered bibliometric transactions. The effect of undefined or dominant self-transaction
is the main problem in the analysis of bibliometric square matrices, and has lead to the
development of special statistical techniques. Figure 6.1 presents a fictitious example for
symmetric bibliometric transaction matrix. The number of references shared by two papers,
the number of joint articles of two units or the number of co-citations express symmetric
relations because the relation between two elements or units is not directed in such cases.
n×n p1 p2 p3  pj  pn
p1 17 0 0  2  1
p2 0 9 3  1  0
p3 0 3 56  0  1
       
pj 2 1 0  14  0
       
pn 1 0 1  0  22
Figure 6.1 Example for a symmetric transaction matrix with dominant main diagonal
(Matrix representing the number of joint references in a given paper set)

82
The information flow expressed by citations given by one unit to another one is not
necessarily reflecting mutual relationship. The same applies to the attendance of countries at
international conferences. Cross-citations matrices and attendance at meetings or mobility are
typical examples for non-symmetric transaction matrices. An example taken from Schubert et
al. (1983) is shown by Figure 6.2.
n×n US UK DE  SU  IN
US 4026 310 350  80  56
UK 617 988 220  48  32
DE 385 152 436  44  9
       
SU 22 8 17
 113  3
       
IN 159 21 28  6  242
Figure 6.2 Example for a non-symmetric transaction matrix with dominant main diagonal
(Matrix representing the number of attendees at international conferences)
Figure 6.3, finally presents an example for incomplete transaction matrices. The number of
internationally co-authored publications between a country and itself country is not defined.
Nevertheless, the missing main diagonal of the transaction matrix is often replaced by the
total number of papers of the corresponding country in order to be able to calculate Salton’s
measure of the Jaccard Index on the basis of the matrix. All elements of the main diagonal of
the resulting ‘similarity’ matrix are equal to 1, and have no particular meaning and
interpretation.
n×n US UK DE  RU  IN
US • 328 374  128  78
UK 328 • 74  44  5
DE 374 74 •  95  22
       
RU 128 44 95  •  3
       
IN 78 5 22  3  •
Figure 6.3 Example for a symmetric transaction matrix with undefined main diagonal
(Matrix representing the number of international co-publications)

83
As mentioned above, bibliometric transaction matrices can be symmetric or non-symmetric.
The latter ones can be symmetrised by the following transformation: B = ½·(A + AT), where
A is the original non-symmetric matrix and B is the symmetrised transaction matrix.

84
6.2 Bibliographic coupling and co-citation analysis
The most important bibliometric method based on reference literature is bibliographic
coupling. The concept of bibliographic coupling was proposed more than three decades ago
by Kessler (1964). In a comprehensive validation study by Vladutz and Cook (1984) could be
shown
“that the utilization of bibliographical coupling in very large citation databases is
practically feasible and that in 76% of the cases it yields valid results by
providing for each input publication 2-3 other publications from the same year,
that are closely related by subject”.
Therefore, the method of bibliographic coupling may prove a valuable alternative to other
mapping methods, especially, because this technique is immediately available and applicable
after publication of a body of literature that does not only contain cited documents.
Bibliographic coupling is often confused or wrongly considered equivalent with co-citation
analyses. The latter ones analyse reference pairs, that is, cited papers, whereas bibliographic-
coupling methods proceed from those citing papers that share items in their reference lists.
Both bibliographically linked publications and co-citation links are assumed to form clusters
representing the same or at least related research topics.
We introduce the two techniques with the help of a model suggested by S.K. Sen and S.K.
Gan in 1983 and generalised by Glänzel and Czerwon in 1996. The model can briefly be
described as follows.
The total set of scientific literature generates a Boolean vector space which is, particularly,
defined by the relationship of papers published in a given period and the set of all references
cited by them. Assume that all m references cited in all n papers in question are arranged and
indexed in some order. The elements of the space are Boolean vectors representing the
publications, their j-th component (1 ≤ j ≤ m) takes then the values 1 or 0, according as the
paper cites the references j or not. The document–reference assignment of the total paper set
published in a given period and indexed in some sequence can then be represented by a huge
n×m Boolean matrix A. Without the loss of generality we assume that the rows consist of
the publication (document) vectors di (1 ≤ i ≤ n) and the columns represent the reference
vectors rj (1 ≤ j ≤ m). Figure 6.3 presents an example matrix.
The matrix A in its present form does, so far, not reveal anything about bibliographic links
and their strength. Sen and Gan have, therefore, suggested using the Coupling Angle (CA) as a
coupling measure. It is defined as the cosine of two Boolean vectors di and dj that can be
obtained from their scalar product as follows
CA()dd dd
dd
ij
ij
ij
=⋅
⋅ .
The Coupling Angle CA takes then the value 1 if two Boolean vectors are parallel, and
CA = 0 if they are rectangular. The strength of bibliographic coupling of two papers can thus
be visualised as the angle between the corresponding Boolean vectors. This may help to find
appropriate thresholds based on its geometrical interpretation. Papers represented by
rectangular vectors are independent; those represented by parallel vectors are concerned with
identical topics. Two documents may then be considered to be concerned with a related topic

85
if the angle between the vectors representing the documents does not exceed a given angle ϕ
(0° ≤ ϕ < 90°). For example, the choice of ϕ = 60° results in a threshold CA = 0.5, and the
angle ϕ = 75° corresponds to a threshold CA ≈ 0.25.
Cited papers (references)
n×m r1 r2 r3 r4 r5 r6  rj  rm
C
i
d1 1 0 0 1 0 0
 0  1
t
i
d2 0 0 0 0 1 0
 1  0
n
g
d3 0 1 1 0 0 0
 0  1
p
          
a
p
di 1 0 1 1 0 1
 1  0
e
r
          
s
dn 1 1 0 0 0 1
 0  0
Figure 6.4 A hypothetical Boolean matrix representing the relationship
publications–references
Glänzel and Czerwon (1996) have shown that in the above case the Coupling Angle is
identical with Salton's measure (rij). Thus we have CA(didj) = rij and a 'geometric'
interpretation of Salton's measure in terms of the angles between two Boolean vectors.
Matrices representing bibliographic links and their strength can be readily derived from the
Boolean matrix A as introduced above. The product matrix B = A·AT provides the number of
joint references of the given papers. An example for such a 'bibliographic-link' matrix is given
in Figure 6.4. Finally, the matrix R = Diag(B)–½·B·Diag(B)–½ = [rij] = [CA(didj)] contains
Salton's measure of the strength of the bibliographic link of all pairs of papers.
A more popular definition regards Salton's measure as the ratio of the number of joint
references and the geometric mean of the number of references of the two papers concerned.
Bibliographic coupling is without any restriction a symmetrical relation. Moreover rij takes
the value 1 for the strength of the bibliographic link of any paper with itself. In contrast to
several other bibliometric phenomena such as, e.g., international collaboration, this makes
sense because the relationship of any paper to itself must be considered maximum. These
properties guarantee that Salton's measure is an appropriate measure of the strength of
bibliographic coupling.
The method of co-citation clustering was introduced independently by Small (1973) and
Marshakova (1973). The matrix the elements of which present co-citation links can be
derived from the same Boolean matrix A. Here the Coupling Angle is defined as the cosine of
two Boolean column vectors ri and rj, i.e.,

86
ji
ji
ji rr
rr
rr ⋅
⋅
=)(CA .
The product matrix C = AT·A then provides the number of co-citations of the given papers.
The matrix S = Diag(C)–½·C·Diag(C)–½ = [rij] = [CA(rirj)] contains Salton's measure of the
strength of the co-citation link of all pairs of papers. Note, that C is not simply the transpose
of the corresponding bibliographic coupling matrix B, i.e., C ≠ B.
An alternative measure for the strength of links is the Jaccard Index. It was originally defined
as a measure of the relative intersection of finite sets. In particular, we have
Jij = Ai∩Aj
Ai∪Aj
= nij
ni + nj – nij ,
where Ai and Aj are finite sets with cardinality ni and nj, respectively, and the cardinality of
their intersection is denoted by nij. Also Jij takes its values in the interval [0, 1], where Jij = 0
means that the two sets are disjoint, and Jij = 1 means that the two sets are identical. In the
case of bibliographic coupling each set Ai and Aj represents the set of items in a reference list.
Up to now the technique of bibliographic coupling has been applied very rarely for purposes
of research evaluation. This fact is surprising because the bibliographic coupling concept has
obviously advantages compared with co-citation clustering.
- The most important one is that just published papers that are closely related by
bibliographic coupling links can provide snapshots of early stages of a speciality's
evolution. By contrast, it may take time before a 'critical mass' of papers on a new
research topic is created that is needed to produce the highly cited publications on
which the co-citation mapping is based (Hicks, 1987).
- From the viewpoint of information retrieval, co-citation clustering results in the
restriction to frequently cited papers, whereas bibliographic coupling extends to
practically all publications.
Sharabchiev (1988) has shown that both techniques provide comparable results of the
structure of research front specialities and complement each other. ISI is using combinations
of the two worlds for their products, for instance, SciViz (cf. Small, 1998).
Glänzel and Czerwon (1996) have used bibliographic coupling also to identify core
documents that represent 'hot' and research-front topics. This method makes it possible to
apply bibliographic-coupling techniques to both research evaluation and information retrieval.
6.3 Co-word, Co-heading and Co-author Clustering Techniques
These techniques are based on the analysis of co-occurrences of terms, keywords or subject
headings. Most prominent large-scale product for co-word analysis is LEXIMAP and its
derivates; the used algorithm is LEXINET. This method has been developed in France by
Turner, Callon and Courtial (see, for example, Callon et al., 1983, 1986, Turner et al., 1988,
Law and Whittaker, 1992 and Courtial, 1994). Co-word clustering is also a standard technique
at ISI. Co-word analysis is based on frequency analyses of co-occurrence of keywords

87
extracted from titles, abstracts or text, in general. Since its fields of application are manifold it
has already evolved to an own discipline.
Todorov (1990) has developed a co-heading analysis that is based on co-occurrence of subject
headings used in specified bibliographic databases. He has used the subject classification of
the INSPEC database. His methodology has certain database-specific limitations.
Unlike co-word, co-citation and bibliographic coupling techniques that are above all designed
to describe the structure of science and it evolution at the macro and meso level, co-author
clustering and author co-citation analysis (ACA) are interesting bibliometric methods to
reveal structures at the micro and meso levels (White and McCain, 1998). However, it should
be mentioned that ACA has a serious shortcoming. It is based on first-author co-citation. Both
the sequence of co-authors and the strength of collaboration links are somewhat distorting the
results.
Several authors have shown that the combination of several different methods essentially
improves efficiency and validity of results (cf., Sharabchiev, 1988, Braam et al., 1991).
6.4 Techniques of Matrix Analysis
Basically, the following three techniques can be applied to the analysis of bibliometric
transition matrices.
− Deviation of observations from expectation
− Calculation of distance and similarity measures
− Decomposition of the matrix
The derived measures can be used as bibliometric indicators themselves (e.g., Salton’s
measure, Jaccard Index), or serve as a basis of multivariate analyses such as cluster analysis,
multidimensional scaling, quasi-correspondence analysis etc. These techniques, which are
preferably applied to mapping of the structure and dynamics of science, can be considered an
extension of bibliometric indicators.
Scientometrics transaction matrices have first been analysed by Price (1981). Price has
shown that distorted or censored main diagonals of matrices can uniquely be reconstructed.
Let A = (aij) be an n×n square matrix with n > 2. The basis assumption is that the transaction
matrix A represents an independence model, that is, the transaction levels between the entities
or units are determined by their size only. Consequently, we can write A = p⋅qT for some
appropriate vectors p and q. In particular, we have aij = pi
⋅
qj for all indices I and j (1 ≤ i,
j ≤ n). In case of dominant main diagonal, this model fails, and the aii values might thus be
considered distorted, and can be omitted. Thus we assume that the elements of the main
diagonal are unknown. The products of the known elements over rows and columns are
denoted by ai×’ and a×j’, respectively. a××’ denotes the grand total product of the matrix
omitting the unknown diagonal. Since the vectors p and q and thus their components pi and qj
are unknown, the diagonal elements of A cannot be immediately reconstructed. However,
since under the above assumption a××’ = {Πi pi
⋅
Πj q
j}n-1 and for the corresponding sub-
matrices Akk, a××’kk = {Πi
≠
k pi
⋅
Πj
≠
k qj}n-2 , we have

88
p
k
⋅
qk = (a××’)1/(n–1)/(a××’kk)1/(n–2) for all k = 1,2, … , n.
This formula can be a bit simplified by using the following substitution:
a××’kk = a××’/(ak×’⋅a×k’). Thus, we finally have the following solution
p
k
⋅
qk = (ak×’⋅a×k’)1/(n–2)/(a××’)1/((n–1)·(n–2)) ; k = 1,2, … , n.
Hence we obtain the reconstructed matrix A* = (aij*) with aij* = aij for i ≠ j and
aii*= (ai×’⋅a×i’)1/(n–2)/(a××’)1/((n–1)·(n–2)) .
It is known that the maximum likelihood estimator of the expected number of transactions eij
can be obtained from the observed transactions aij in the following manner.
e
ij = ai+a+j/a++ ,
where ai+ =Σj a
ij, a+j =Σi a
ij and a++ = ΣiΣj aij. If the main diagonal is known and not
dominant, there is from the statistical viewpoint no problem. Then the significance of the
deviation of the observed transactions from the estimated ones can be evaluated on the basis
of the following χ2-statistic
χ2 = ΣiΣj (aij – eij)2/eij.
However, the task is not the evaluation of the goodness-of-fit, namely, of the significance of
the deviation from the independence model but to measure the distance of individual
observations from their expectations. This can be done with the help of correspondence
analysis (CA). This method allows the joint plot of variables in the same diagram (cf. Tijssen
et al., 1988). Figure 6.5 taken from Tijssen et al. (1988) presents a typical application of CA.
Subject fields represented by PACS codes taken from the INSPEC database are jointly
presented with journals in a CA diagram. This diagram largely reflects specialisation of
scientific journals.
Figure 6.5 Correspondence analysis of a journal-to-field matrix in physics in 1985
(according to Tijssen et al., 1988)

89
The indipendence model cannot be assumed if the main diagonal of the transaction matrix is
dominant. The method by Price (1981) does not allow the use of the Pearson statistic
χ2 = ΣiΣj (aij – eij)2/eij since the element of the main diagonal have been determined with the
help of the off-diagonal elements. However, there are several other ways to solve this
problem. The quasi-independence model offers one possibility. According to this model,
elements of the matrix can be ignored and the independence model still fits on the remaining
observations aij, where i and j are elements of a subset L of the index set. Usually,
L = {(i, j); i ≠ j, i, j = 1, 2, … , n} is assumed. A χ2-statistic can be constructed with
restriction to L. The quasi-correspondence analysis (QCA) can then be conducted in
analogous manner to the CA. A comprehensive description of the QCA can be found, for
instance, in the papers by de Leeuw and van der Heijden (1985) and Tijssen et al. (1987).
Figure 6.6 presents a typical application of QCA to cross-journal citation analysis. The main
diagonal in cross-citation matrices is usually heavily distorted by the large share of self-
citations.
Figure 6.6 Quasi-correspondence analysis of a cross-citation matrix in physics in 1985
(italics: citing journals, bold: cited journals; according to Tijssen et al., 1988)
A second possibility to eliminate dominant main diagonals is an appropriate decomposition.
In the paper on attendance at international scientific meetings Schubert et al. (1985) have
suggested the following decomposition. The transaction matrix A can be decomposed into a
sum of a dyadic product of appropriate vectors p and q representing the independence model
and a diagonal matrix C representing surplus self-transactions. According to this approach,
we have
A = p⋅qT + C.
Analogously to the previous solution, the algorithm is based on an iteration method. The
results can be analysed on the basis of the deviation from their expectation, and be visualised
in relational charts. Moreover, the elements of the main diagonal of the matrix C reveal
interesting additional information on self-transactions.

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7. THE BORDERLAND OF BIBLIOMETRIC RESEARCH
7.1. Linkage Between Science and Technology
On Tuesday, 13 May, 1997 a spectacular article entitled “Study Finds Public Science is Pillar
of Industry" appeared in the Science Times Section of the New York Times (Broad, 1997).
This article was based on results published in a study for the National Science Foundation for
which CHI traced more than 45,000 references from U.S. patents to the underlying research
papers. Narin (CHI) found that more than 70 percent of the scientific papers cited on the front
pages of U.S. Industry patents came from public science (science performed at universities,
government labs, and other public agencies. This implies that public science has a direct,
massive impact on industrial technology. Narin also found that this dependence is increasing
rapidly, more than tripling in the six years from 1987/88 to 1993/94.
To measure the direct impact of science on technology with bibliometric means is a difficult
task. Studies on the citation gap in applicable sciences (Vanels et al., 1989, Jansz and LePair,
1992, Jansz, 1999) have pointed to this problem. According to these studies communication
patterns in these areas do not primarily rely on publications in scientific journals or, in some
fields, in patents. The analysis of patents by bibliometric means can, however, help to study
quantitative aspects of research at the borderline between science and technology. The
combination between publication and patent analysis can be useful in such subject areas, and
can thus improve the validity of the bibliometric studies.
Unlike the publication analysis where most methodological questions are solved, several
methodological aspects of patent analyses are still controversy.
Patent analyses are based on relevant information that can be retrieved from the patent
databases. The databases of the United States Patent and Trademark Office (USPTO) and of
the European Patent Office (EPO) are probably the most frequently used databases for
analyses of patent-literature links. Moreover, patent information can be also retrieved from
the bibliographic database Chemical Abstract that indexes subject-relevant patents, too. In the
following table, most important information used in bibliometrics is shown. This information
is usually organised in corresponding search fields.
Relevant information from patent databases:
Patents
1. Patent identification
2. Names of inventors
3. Assignee
4. Addresses
5. References (patents and other publications)
6. Abstract
7. Classification
Figure 2.3 gives an example for patent information provided by the USPTO.

91
PATN
WKU 062637363
SRC 9
APN 4049543
APT 1
ART 286
APD 19990924
TTL Electrostatically tunable resonance frequency beam utilizing a stress-sensitive film
ISD 20010724
NCL 27
ECL 1
EXP Moller; Richard A.
NDR 7
NFG 16
INVT
NAM Thundat; Thomas G.
CTY Knoxville
STA TN
INVT
NAM Wachter; Eric A.
CTY Oak Ridge
STA TN
INVT
NAM Davis; J. Kenneth
CTY Kingston
STA TN
ASSG
NAM UT-Battelle, LLC
CTY Oak Ridge
STA TN
COD 02
CLAS
OCL 7351436
XCL 7351434
XCL 7351426
XCL 310309
XCL 361280
EDF 7
ICL G01P 1500
FSC 73
FSS 514.36;514.34;514.26;514.17;514.18
FSC 310
FSS 309
FSC 361
FSS 280;283.1;287
UREF
PNO 5211051
ISD 19930500
NAM Kaiser et al.
OCL 73 1D
UREF
PNO 5267471
ISD 19931200
NAM Abraham et al.
OCL 73105
UREF
PNO 5719324
ISD 19980200
NAM Thundat
UREF
PNO 5918263
ISD 19990600
NAM Thundat
OREF
PAL G. Y. Chen, et al "Adsorption-Induced Surface Stress & Its Effects on
-- Resonance Frequency of Microcaltilevers" J.Appl.Phys. 77 (8), Apr. 1995, 1-5.
PAL M. Ilavsky et al, Responsive Gels: Volume Transitions I Editor: K. Dusek, 1993.
LREP
FR2 Marasco; Joseph A.
ABST
PAL Methods and apparatus for detecting particular frequencies of acoustic
-- vibration utilize an electrostatically-tunable beam element having a
-- stress-sensitive coating and means for providing electrostatic force to
-- controllably deflect the beam element thereby changing its stiffness and
-- its resonance frequency. It is then determined from the response of the
-- electrostatically-tunable beam element to the acoustical vibration to
-- which the beam is exposed whether or not a particular frequency or
-- frequencies of acoustic vibration are detected.
GOVT
PAR The United States Government has rights in this invention pursuant to
-- contract no. DE-AC05-96OR22464 between the United States Department of
-- Energy and Lockheed Martin Energy Research Corporation.
Figure 7.1 Complete information about a patent by Thundat et al. (2001) according to the
USPTO database

92
Links between science and technology can basically studied on the basis of the following
biblio-technometric relations.
• References to scientific publications in patents
• References to patents in scientific publications (so-called reverse patent citations)
• Authors-inventor relations
Links established through patent citations to scientific literature are considered most
important, and is therefore most frequently applied (see, for instance, Narin et al., 1997,
Verbeek et al., 2002). Nevertheless, also the reverse linkage, established by citation to patents
in scientific literature uncovers interesting aspects of science-technology links (see, for
instance, Hicks, 2000, Glänzel and Meyer, 2002). The high relevance of patents in chemistry
research, among others, reflected by indexing patents in the Chemical Abstracts bibliographic
database, could be also confirmed by Glänzel and Meyer (2002).
The third issue is probably the most promising one, however, it results in some, partially
unresolved technical problems. The correct identification of inventors as authors of scientific
publication in large-scale analyses is almost unfeasible. Nevertheless, at lower levels of
aggregations or in specific domains, reliable studies of this relationship can be conducted (cf.,
Noyons et al., 1994).
7.2. New horizons: bibliometric methods in webometrics
In bibliometrics publications are considered the elementary units of scientific information and
the main source of indicators. The diversity of new patterns of communication on the
electronic network and the heterogeneity of the internet, however, blurs the traditional
frontiers between formal and informal communication. According to Björneborn and
Ingwersen (2001) point out, that the web is an information space quite different from common
scientific and professional databases, the similarities between electronic and print medium are
often superficial. In particular, they write:
“Obviously, the breakthrough for everybody to express themselves, practically
without control from authorities, to become visible world wide, also by linking to
what pages one wants to link, to assume credibility by being ‘there’, and to obtain
access to data, information, values and knowledge in many shapes of and degrees
of truth, has generated an a reality of freedom of information, also in regions and
countries otherwise poor of infrastructure.”
The most important difference between print media and the web is that time plays a different
role on the web. An additional fundamental difference between print and web based analysis
is the possibility of an almost continuous change of contents on the web (Glänzel, 2001/2003)
resulting in a completely different notion of ageing of information.
Although the analogy between bibliometric and webometrics phenomena is limited, several
bibliometric measures and models can be applied in webometrics, too. In the following, we
briefly summarise possible web-based measures.
- The number of visitors of web sites can be described by point processes or pure birth
processes being one of the rare cumulative process on the web.
- The frequency of downloads can be described by informetric models used in the
context of copy requests.

93
- Sitation and co-sitation analyses have already been conducted. There are analogies
but also deviations from the bibliometric (co-) citation models (Rousseau, 1997,
Björneborn and Ingwersen, 2001, Glänzel, 2001/2003).
- ‘Webographic coupling’ might be a promising tool for depicting structures of and
identifying cluster in the web.
- The possible analysis of (co-)sponsorship has no real counterpart in bibliometrics.
- Studies of ‘small world’ phenomena (see, i.e., Watts and Strogatz, 1998) are more
relevant in webometrics than in bibliometrics where little has been done in this area.
- Analysis and mapping of network structures on the web. In this context many formal
statistical techniques also used in bibliometrics can be applied.
In all, we can conclude that structures on the Web are more complex than their bibliographic
‘counterparts’. However, the main difference between print and web medium can be
summarised as follows. Most bibliometric processes are cumulative since publications
(except for the extremely rare cases of retractions) and citations are irreversible and
bibliographic links cannot be removed if they have once been established. By contrast, the
Web is in terms of both, content and links in permanent change.

94
8. INTRODUCTION INTO BIBLIOMETRIC TECHNOLOGY
8.1 Outlines of cleaning-up and computerised data processing of bibliographic data
In the following we give an example for computerised data processing to visualise the way
from bibliographic data to bibliometric indicators. To process all bibliometric indicators
needed for the comparative studies, to calculate the necessary statistical functions, to fit the
underlying frequency distributions and to estimate their parameters the development of
appropriate bibliometric software systems is necessary. The first step in data processing is
usually the process of downloading or extracting data from bibliographic databases. The
downloaded data cannot immediately be processed into indicators. Due to spelling variances
and errors, these data have to be carefully cleaned up. Basically four main sources of errors
can be identified.
- the authors of the publications indexed in the database
- the editors of the journals covered by the database
- the database producer
- the user of the database
The authors themselves are responsible for many errors. Among these errors, we find, above
all, misspelling, incomplete or wrong addresses and incorrect citations. These errors can
practically not be corrected, except for the level of individual publications provided that the
full text of all papers involved are available. The following example might illustrate this quite
dramatic effect. The paper by Schubert, Glänzel and Braun (1989) “Scientometric datafiles. A
Comprehensive set of indicators on 2649 journals and 96 countries in all major science fields
and subfields, 1981-1985” published in Scientometrics, vol. 16, pp. 3-478 has received 137
citations. Among those are 113 correct citations, whereas 24 citations were incorrect. The
error caused by citing authors amounts to 17.5%. We can detect three particular types of
errors; the most frequent was the incorrect or missing page number, followed by an incorrect
publication year and the incorrect first author. The head of a research group or institute is
sometimes erroneously assumed to be the first authors. All variances of the cited work that
occurred in the Web of Science database are presented in Figure 8.1.
Cites 1st author Journal VOL BP PY
113 SCHUBERT A SCIENTOMETRICS 16 3 1989
3 SCHUBERT A SCIENTOMETRICS 16 3 1988
1 SCHUBERT A SCIENTOMETRICS 16 3 1987
2 BRAUN T SCIENTOMETRICS 16 3 1989
12 SCHUBERT A SCIENTOMETRICS 16 11989
1 SCHUBERT A SCIENTOMETRICS 16 81989
1 SCHUBERT A SCIENTOMETRICS 16 18 1989
1 SCHUBERT A SCIENTOMETRICS 16 218 1989
1 SCHUBERT A SCIENTOMETRICS 16 239 1989
1 SCHUBERT A SCIENTOMETRICS 16 432 1989
1 SCHUBERT A SCIENTOMETRICS 16 1989
Figure 8.1 Example for an incorrectly cited publication

95
Temp002
Journal
codes
Source
data Corporate
address
Citation
data
WGSRC01 WGADDR01 WGCIT01
WGJRNL01
Country
codes
WGSRC02
Journal coding and
subject assignment
Temp001
Citation
count
Sort by
cluster-key
De-duplication
and counting
Sort by
cluster-key
Temp003
Source/
Citation
SRC&CIT Matching source
and citation data
by cluster-key
Sort by journal
Temp004
Journal
impact
Macro and
Journal
Indicators
(Master files)
WGIND01
Subject
Categories
(S)SCI Database
On-line CD-EditionMagnetic tape
WGINDxx
Publication activity and
citation impact statistics
Bibliostat
Figure 8.2 Simplified flow chart of computer processing of bibliometric indicators

96
Editorial policy is also responsible for a certain share of errors. Omitted addresses or
truncated references are among such errors. These errors cannot be corrected by manual or
computerised standard procedures.
Errors caused by the database producers are twofold; errors during data recording are hard to
detect. However, these errors have from the statistical viewpoint not much weight. Systematic
errors due to the policy in preparing the database have sometime sever consequences, but can
often be corrected by users. The case of Angewandte Chemie – International Edition may just
serve as one example (see, Braun and Glänzel, 1995, and van Leeuwen et al., 1997).
Unfortunately, there are also errors caused by the user. Standardisation of data processing
techniques, the exchange of results among bibliometric research centres (cf. Glänzel, 1996)
and co-operation as the best solution to developing common standards (cf. Katz, 1996) might
help to reduce errors caused by users to the minimum.
Figure 8.2 and 8.3 present a overview of main steps of processing of bibliographic data to
indicators.
Macro and
Journal
Indicators
(Master files)
Bibliostat
Obsolescence statistics
and empirical citation rate
distributions and processes
IRWIN for Windows
Program for the analysis
of bibliometric distributions
LUPUS for Windows
Visual interface for
bibliometric indicators
Bibliostat
Publication activity
and citation-based
statistics
Figure 8.3 Outline of statistical applications
The program Lupus – Visual Bibliometrics developed by Glänzel in 1995 is designed for the
use in addition to the CD-ROM edition of the (S)SCI of the Institute for Scientific
Information (ISI). The software is compatible to the annual cumulations of the CD-Edition.
Visual Bibliometrics calculates and visualises basic and more advanced macro-indicators.
Besides the main window five charts and maps can be chosen according as which indicator is
to be visualised. The main window displays the most important bibliometric macro-indicators
at the national level if the fields Selected country, Selected field and Publication year have
valid entries. Besides the set of displayed bibliometric indicators a country profile summarises
bibliometric performance characteristics. Figure 8.4 through 8.7 show the main features of
this add-on.

97
Figure 8.4 The main window presenting bibliometric “standard” indicators
and a concise country profile
Figure 8.5 Bar diagrams show the extent of international scientific collaboration
in the selected field
Figure 8.6 The relational chart shows the plot of observed vs. expected citation rate
in the selected field

98
Figure 8.7 The “bibliometric atlas” visualises the most important publication activity
and citation impact indicators
8.2 Bibliometric Software
In this last section, we will give four examples for bibliometric software; two of them are
freeware, the other two packages are commercial products.
The Bibliometrics Toolbox
The Bibliometrics Toolbox was the first bibliometric programme package. It has been created
by Terrence A. Brookes to assist bibliometricians in preparing statistics from their
downloaded data. It comprises a set of computer programs written in Turbo Pascal that
measure the bibliometric aspects of a literature such as Bradfordity, productivity ranks, degree
of clustering, and indices of concentration. Bibliometrics Toolbox has been reviewed by
McLain (1990), and is freeware available from the FTP address.
Data view bibliometric software for analysis of downloaded data
Data view is commercial software. It has been developed by the Centre de Recherche
Rétrospective de Marseille (CRRM,) at the Faculté Saint Jérome in Marseille (France). The
software does not provide a new bibliometric method; it provides a bridge between
information sources and the various data analysis methods. Dataview is designed as a
software tool for experts of scientific and technological information processing. They can use
this tool to build their own analysing techniques according to the most suitable statistic
methods. In order to reach this purpose, dataview accepts various formats of information
funds such as on-line databases or CD-Editions, allows the use of several types of
bibliometric items in the same study and provides numerical data for various statistical
techniques. Dataview provides the main necessary issues and the main necessary edition
formats used for bibliometric analysis. The main features of this software are visualised in
Figure 8.8. For more details, consult Rostaing et al. (1993).

99
Figure 8.8 Main features of the bibliometric software ‘Dataview’
Bibexcel
Bibexcel is a toolbox developed by Olle Persson, Inforsk, Umeå Univ (Sweden). This
software is designed to assist a user in analysing bibliographic data, or any data of a textual
nature formatted in a similar manner. The idea is to generate data files that can be imported to
MS Excel, or any program that takes tabbed data records, for further processing. This toolbox
includes a number of tools, some of them visible in the window and others hide behind the
menus. Many of the tools can be used in combination to achieve the desired result. Figure 8.9
shows the main window of Bibexcel.
Bibexcel allows generating several maps using Multi-Dimensional-Scaling techniques. A map
is made by first calculating the number of times pairs of units, for example authors, co-occur
in the document records. Then the resulting co-occurrence matrix is taken as input to a Multi-
Dimensional-Scaling program that finds the best fitting two-dimensional representation of the
input values. The distance between units on the map is inversely proportional to the number
of co-occurrences, which means that the more two units co-occur the closer they will be
located on the map. The maps presented in Figures 8.10 and 8.11 are examples by the author
of Bibexcel.

100
Figure 8.9 The main window of Bibexcel
Figure 8.10 Intellectual base of scientometrics 1978–1999. First author co-citations made by
1062 papers in the journal Scientometrics (redrawn from Persson, 2000)
Figure 8.11 visualises first author co-citations made by 1062 papers in the journal
Scientometrics. This is based on the ACA method suggested by White and McCaine (1998).
The units are represented by labels, which can be coloured to show a certain attribute, for
example the national origin of an author. A circle can be drawn at each node indicating its
size, for example the number of papers written by an author. Lines between nodes as well as
their thickness indicate the number of co-occurences. This example has been taken from
Persson (2000).

101
The second example given in Figure 8.11 shows the collaboration among main institutions in
Finland on the basis of co-publications. The location of institutions on the map is estimated by
applying a Multi-Dimensional-Scaling algorithm to a collaboration matrix. This example has
been taken from Persson et al. (2000).
Bibexcel is freeware, and can be downloaded from the author’s homepage.
Figure 8.11 Collaboration among main institutions (according to Persson et al., 2000)
BibTechMonTM
BibTechmon is the last example for bilbliometric software. It is commercial product
developed at the Austrian Research Centres Seibersdorf (Austria). BibTechMon can be used
for the documentation and structuring of external information from patent and bibliographic
databases, from the internet or other external or internal sources. The software has the
following main features. It supports the process of building a literature database as well as
designing knowledge maps and analysis of the content by
• reading in documents for building up an internal database
• automatic indexing for identification and classification of relevant key-terms
• calculation of knowledge maps
• analysis of the maps using an interactive surface or browser
• direct access to the documents in a database
• database search functions

102
Figure 8.12 Knowledge map of key terms (top) and location of various key terms (bottom)
forevolutionary economics

103
Figure 8.12 taken from Dachs et al., 2001 presents knowledge map and location of key terms
for ‘evolutionary economic’. The authors have retrieved literature from the EconLit database.
Data have been cleaned up by removing distortions based on the context sensitive
longest-match principle and a phrase recognition algorithm (Widhalm et al., 1999). This
automatic indexing module has been applied to titles, sources and abstracts of each record.
The mapping algorithm for the co-word analysis is based on the Jaccard Index as similarity
measure. Maps are then generated applying an MDS algorithm. The underlying mathematical-
statistical procedure is decribed by Kopsa and Seibel (1998). Further information about this
software and its fields of application can be found, for instance, on Clemens Widhalm’s home
page.

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APPENDIX
RECOMMENDED READINGS
I. Fundamental works
1. Price, D. de Solla 1961, Science since Babylon, Yale Univ. Press, New Haven.
2. Price, D. de Solla 1963, Little Science, Big Science, Columbia Univ. Press, New York.
3. Pritchard, A. 1969, Statistical bibliography or bibliometrics? Journal of Documentation
24, 348-349.
4. van Raan, A.F.J. (Ed.) 1988, Handbook of Quantitative Studies of Science and
Technology, North-Holland, Amsterdam.
5. Ziman, J. 1984, An Introduction to Science Studies - The Philosophical and Social Aspects
of Science and Technology. Cambridge University Press, Cambridge.
II. Bibliometric methods developed for science studies
6. Callon, M., Courtial, J.P., Turner, W.A. and Bauin, S. 1983, From translations to
problematic networks: An introduction to co-word analysis, Social Science Information
22, 191-235.
7. Carpenter, M. P. and Narin, F. 1981, The adequacy of the Science Citation Index (SCI) as
an indicator of international scientific activity, Journal of the American Society for
Information Science 32, 430-439.
8. Garfield, E. and Welljams-Dorof, A. 1992, Citation data: their use as quantitative
indicators for science and technology evaluation and policy-making, Science and Public
Policy 19, 321-327.
9. Glänzel, W. and Czerwon, H.J. 1996, A new methodological approach to bibliographic
coupling and its application to the national, regional and institutional level, Scientometrics
37, 195-221.
10. Glänzel, W., Schubert, A., Czerwon, H. J., An Item-by-item Subject Classification of
Papers Published in Multidisciplinary and General Journals Using Reference Analysis,
Scientometrics, 44, 1999, 427-439.
11. Hicks, D. 1987, Limitations of co-citation analysis as a tool for science policy, Social
Studies of Science, 17, 295-316.
12. Irvine, J. and Martin, B. R. 1989, International comparisons of scientific performance
revisited, Scientometrics 15, 369-392.
13. Moed, H.F., de Bruin, R. E. and van Leeuwen, Th. N. 1995, New bibliometric tools for
the assessment of national research performance: Database description, overview of
indicators and first applications, Scientometrics, 33, 381-422.
14. Schubert, A. and Braun, T. 1986, Relative indicators and relational charts for comparative
assessment of publication output and citation impact, Scientometrics, 9, 281-291.
15. Schubert, A. and Braun, T. 1992, Standards for citation based assessments,
Scientometrics, 26, 21-35.

113
16. Small, H.G. 1973, Co-citation in scientific literature. A new measure for the relationship
between publications. JASIS, 24, 265-269.
17. Small, H.G. and Griffith, B. C. 1974, The structure of scientific literatures I: Identifying
and graphing specialities, Science Studies 4, 17-40.
III. Selected comparative studies based on science indicators
18. Glänzel, W. 1996, Scientometric Indicators Datafiles. A bibliometric approach to social
sciences. National research performances in 6 selected social science areas, 1990-1992,
Scientometrics, 35, 291-307
19. Martin, B. R., Irvine, J. and Isard, P. 1990, Trends in UK government spending on
academic and related research: a comparison with FR Germany, France, Japan, the
Netherlands and USA, Science and Public Policy 17, 3-13.
20. Miquel, J. F., Ojasoo, T., Okubo, Y., Paul, A., Doré, J. C. 1995, World science in 18
disciplinary areas: Comparative evaluation of the publication patterns of 48 countries over
the period 1981-1992, Scientometrics, 33, 149-167
21. Glänzel, W., Science in Scandinavia: A Bibliometric Approach, Scientometrics, 48, 2000
121-150 (Correction: Scientometrics, 49, 2000, 357)
22. Schubert, A., Glänzel, W., Braun, T. 1989 World flash on basic research: Scientometric
datafiles. A Comprehensive set of indicators on 2649 journals and 96 countries in all
major science fields and subfields, 1981-1985, Scientometrics, 16, 3-478.
IV. Research in industries
23. Frumau, C.C.F. 1992, Choices in R&D and business portfolio in the electronics industry:
What the bibliometric data show, Research Policy, 21, 97-124.
24. Godin, B. 1996, Research and the practice of publication in industries, Research Policy,
25, 587-606.
25. Grupp, H. 1990, On the supplementary functions of science and technology indicators,
Scientometrics, 19, 447-472.
26. Hicks, D., Ishizuka, T., Keen, P. and Sweet, S. 1994, Japanese corporations, scientific
research and globalization, Research Policy, 23, 375-384.
27. Narin, F. and Rozek R.P. 1988, Bibliometric analysis of U.S. pharmaceutical industry
research performance, Research Policy, 17, 139-154.
V. International scientific collaboration
28. deB. Beaver, D., Rosen, R. 1978, Studies in scientific collaboration. Part I. The
professional origins of scientific co-authorship, Scientometrics, 1, 65-84
29. deB. Beaver, D., Rosen, R., 1979, Studies in scientific collaboration. Part II. Scientific
co-authorship, research productivity and visibility in the French elite, Scientometrics, 1,
133-149
30. Braun, T., Gómez, Isabel, Méndez, Aida, Schubert, A., 1992, World flash on basic
research: International co-authorship patterns in physics and its subfields, 1981-1985,
Scientometrics, 24, 181-200.

114
31. Gómez, I., Fernández, M. T. and Méndez, A. 1995, Collaboration patterns of Spanish
scientific publications in different research areas and disciplines, In: Proceedings of the
Biennial Conference of the International Society for Scientometrics and Informetrics
(ed. by M.E.D. Koenig and A. Bookstein), Learned Inf., Medford, NJ, pp. 187-196.
32. Hicks, D. and Katz, J.S. 1996, Science policy for a highly collaborative science system,
Science and Public Policy, 23, 39-44.
33. Lewison, G. and Cunningham, P. 1991, Bibliometric studies for the evaluation of trans-
national research, Scientometrics, 21, 223-244.
34. Luukkonen, T., Persson, O., Silvertsen, G. 1992, Understanding patterns of international
scientific collaboration, Science, Technology & Human Values, 17, 101-126
35. Luukkonen, T., Tijssen, R. J. W., Persson, O., Silvertsen, G. 1993, The measurement of
international scientific collaboration, Scientometrics, 28, 15-36.
36. Moed, H.F., de Bruin, R.E., Nederhof, A.J. and Tijssen, R.J.W. 1991, International
scientific co-operation and awareness within the European Community: problems and
perspectives, Scientometrics, 21, 291-311.
37. Narin, F., Stevens, K. and Whitlow, E.S. 1991, Scientific co-operation in Europe and the
citation of multinationally authored papers, Scientometrics, 21, 313-323.
38. Vinkler, P. 1993, Research Contribution, Authorship and Team Cooperativeness.
Scientometrics, 26, 213-230
VI. Science in developing countries
39. Arunachalam, S. and Garg, K. C. 1986, Science on the periphery - a scientometric
analysis of science in the ASEAN countries, Journal of Information Science, 12, 105-117.
40. Arvanitis, R., Gaillard, J. (Eds) 1992, Science Indicators for Developing Countries,
ORSTOM, Paris
41. Gibbs, W.W. 1995, Lost science in the Third World, Scientific American, 273, 76-83.
42. Moravcsik, M.J. 1985, Applied scientometrics: An assessment methodology for
developing countries, Scientometrics, 7, 165-176
43. Sancho, R. 1992, Misjudgements and shortcomings in the measurement of scientific
activities in less developed countries, Scientometrics, 23, 221-233.
44. Stolte-Heiskanen, V. 1986, Evaluation of scientific performance on the periphery, Science
and Public Policy, 13, 83-88.
Additional recommended literature
Braun, T., Bújdosó, E., Schubert, A., 1987, Literature of analytical chemistry:
a scientometric evaluation, CRC Press, Inc., Boca Raton, Florida.
Tijssen, R. J. W., 1992, Cartography of science: scientometric mapping with multi-
dimensional scaling techniques. DSWO Press, Leiden University
Noyons, E.C.M., 1999, Bibliometric mapping as a science and research management tool.
DSWO Press, Leiden University
Wouters, P., 1999, The citation culture, PhD Thesis, Private edition.

115
White, H.D., McCain, K.W., 1989. Bibliometrics. Annual Reviews of Information Science
and Technology, 24, 119-186.
Garfield, E., 1998, From citation indexes to infometrics: Is the tail now wagging the dog?
Libri, 48, 67-80.
Borgman, C.L., 1990, Scholarly communication and bibliometrics, Sage.
White, H.D., McCain, K.W., 1998, Visualizing a discipline. An author co-citation analysis
of Information science, 1972-1995. Journal of the American Society for Information
Science, 49, 327-355.
Persson, O., 1994, The intellectual base and research fronts of JASIS 1986-1990. Journal
of the American Society for Information Science, 45, 31-38.